the 20 isometry classes of irreducible [21,9,7]_2 codes are: code no 1: ================ 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 576 and is strongly generated by the following 6 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 0 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 , 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (12, 13), (5, 6, 14)(7, 18, 11)(8, 10, 20)(9, 17, 21)(15, 16, 19), (4, 17, 9)(5, 18, 15)(6, 10, 7)(8, 14, 16)(11, 20, 19)(12, 13), (4, 10)(5, 18)(6, 16)(7, 19)(8, 20)(9, 11)(12, 13)(14, 17)(15, 21), (2, 3)(4, 9)(5, 15)(6, 8)(7, 14)(10, 16)(11, 20)(12, 13), (1, 2)(5, 6)(7, 18)(8, 16)(9, 17)(10, 15)(19, 20) orbits: { 1, 2, 3 }, { 4, 9, 10, 21, 17, 11, 8, 6, 16, 15, 14, 18, 19, 20, 5, 7 }, { 12, 13 } code no 2: ================ 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 the automorphism group has order 36 and is strongly generated by the following 4 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 , 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (4, 5)(6, 14)(7, 15)(8, 9)(10, 17)(12, 21)(16, 18), (2, 3)(6, 14)(7, 16)(8, 10)(9, 17)(11, 19)(15, 18), (1, 14, 6)(2, 18, 16)(3, 7, 15)(4, 17, 9)(5, 8, 10), (1, 18, 15)(2, 7, 6)(3, 14, 16)(4, 9, 17)(11, 19, 20) orbits: { 1, 6, 15, 14, 7, 18, 3, 16, 2 }, { 4, 5, 9, 17, 10, 8 }, { 11, 19, 20 }, { 12, 21 }, { 13 } code no 3: ================ 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 the automorphism group has order 192 and is strongly generated by the following 5 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 1 1 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 1 1 1 1 0 0 0 1 , 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (4, 8)(5, 15)(6, 9)(7, 14)(10, 19)(11, 16)(17, 18), (2, 19, 10)(3, 4, 8)(5, 15, 20)(6, 11, 18)(9, 17, 16), (2, 20)(5, 19)(6, 17)(7, 14)(9, 18)(10, 15)(11, 16)(12, 21), (1, 17, 9)(2, 11, 20)(3, 10, 5)(4, 6, 19)(8, 15, 18), (1, 15)(2, 16)(3, 6)(4, 17)(7, 14)(8, 10)(18, 19) orbits: { 1, 9, 15, 6, 16, 18, 17, 5, 10, 8, 4, 3, 11, 2, 19, 20 }, { 7, 14 }, { 12, 21 }, { 13 } code no 4: ================ 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 the automorphism group has order 36 and is strongly generated by the following 5 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 1 0 1 1 1 0 0 1 0 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 , 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 0 1 , 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 1 1 1 0 1 0 1 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (4, 8)(5, 15)(6, 9)(7, 14)(10, 19)(11, 16)(17, 18), (4, 5, 6)(8, 9, 15)(10, 19, 20)(11, 21, 16)(12, 17, 18), (2, 3)(4, 9)(5, 15)(6, 8)(7, 14)(10, 16)(11, 19)(20, 21), (1, 3)(4, 8)(5, 9)(6, 15)(7, 14)(10, 17)(12, 20)(18, 19), (1, 3, 2)(4, 5, 6)(8, 15, 9)(10, 16, 17)(11, 18, 19)(12, 20, 21) orbits: { 1, 3, 2 }, { 4, 8, 6, 9, 15, 5 }, { 7, 14 }, { 10, 19, 20, 16, 17, 11, 18, 21, 12 }, { 13 } code no 5: ================ 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 1 the automorphism group has order 48 and is strongly generated by the following 5 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 0 1 , 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 ) acting on the columns of the generator matrix as follows (in order): (5, 6, 14)(7, 9, 15)(10, 12, 19)(11, 16, 21)(17, 20, 18), (4, 8)(5, 15)(6, 9)(7, 14)(10, 19)(11, 16)(17, 18), (1, 3)(4, 8)(5, 9)(6, 15)(7, 14)(10, 17)(12, 20)(18, 19), (1, 5, 15)(2, 11, 16)(3, 9, 6)(4, 18, 10)(8, 19, 17), (1, 9, 14)(2, 11, 21)(3, 5, 7)(4, 19, 20)(8, 18, 12) orbits: { 1, 3, 15, 14, 6, 7, 9, 5 }, { 2, 16, 21, 11 }, { 4, 8, 10, 20, 17, 12, 19, 18 }, { 13 } code no 6: ================ 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 192 and is strongly generated by the following 6 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 1 1 0 1 1 0 0 1 1 0 1 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 ) acting on the columns of the generator matrix as follows (in order): (12, 13), (5, 14, 6)(7, 11, 18)(8, 20, 10)(9, 21, 17)(15, 19, 16), (4, 9, 17)(5, 15, 18)(6, 7, 10)(8, 16, 14)(11, 19, 20), (4, 16, 19)(5, 18, 21)(6, 17, 20)(7, 8, 9)(10, 11, 14), (4, 16, 15)(5, 10, 9)(6, 18, 8)(7, 14, 17)(11, 21, 20), (2, 3)(6, 14)(7, 16)(8, 10)(9, 17)(11, 19)(12, 13)(15, 18) orbits: { 1 }, { 2, 3 }, { 4, 17, 19, 15, 21, 9, 6, 14, 11, 16, 5, 18, 8, 10, 20, 7 }, { 12, 13 } code no 7: ================ 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 36 and is strongly generated by the following 4 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 ) acting on the columns of the generator matrix as follows (in order): (12, 13), (3, 21)(4, 11)(5, 9)(6, 17)(7, 18)(10, 19)(15, 20), (2, 3)(4, 9)(5, 15)(6, 8)(7, 14)(10, 16)(11, 20)(12, 13), (2, 5, 9)(3, 4, 15)(6, 17, 8)(7, 14, 18)(11, 21, 20)(12, 13) orbits: { 1 }, { 2, 3, 9, 21, 15, 5, 4, 11, 20 }, { 6, 17, 8 }, { 7, 18, 14 }, { 10, 19, 16 }, { 12, 13 } code no 8: ================ 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (4, 5)(6, 14)(7, 15)(8, 9)(10, 17)(12, 21)(16, 18), (2, 3)(6, 14)(7, 16)(8, 10)(9, 17)(11, 19)(15, 18) orbits: { 1 }, { 2, 3 }, { 4, 5 }, { 6, 14 }, { 7, 15, 16, 18 }, { 8, 9, 10, 17 }, { 11, 19 }, { 12, 21 }, { 13 }, { 20 } code no 9: ================ 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 the automorphism group has order 6 and is strongly generated by the following 2 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (4, 9, 17)(5, 15, 18)(6, 7, 10)(8, 16, 14)(11, 19, 20), (2, 3)(6, 14)(7, 16)(8, 10)(9, 17)(11, 19)(15, 18) orbits: { 1 }, { 2, 3 }, { 4, 17, 9 }, { 5, 18, 15 }, { 6, 10, 14, 7, 8, 16 }, { 11, 20, 19 }, { 12 }, { 13 }, { 21 } code no 10: ================ 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 the automorphism group has order 24 and is strongly generated by the following 4 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 , 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (4, 8)(5, 15)(6, 9)(7, 14)(10, 19)(11, 16)(17, 18), (2, 10, 19)(3, 8, 4)(5, 20, 15)(6, 18, 11)(9, 16, 17), (2, 20)(4, 8)(5, 10)(6, 18)(9, 17)(12, 21)(15, 19), (1, 13)(2, 9, 10, 16, 19, 17)(3, 4, 8)(5, 6, 20, 18, 15, 11)(7, 21)(12, 14) orbits: { 1, 13 }, { 2, 19, 20, 17, 10, 15, 16, 5, 6, 18, 9, 11 }, { 3, 4, 8 }, { 7, 14, 21, 12 } code no 11: ================ 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 the automorphism group has order 12 and is strongly generated by the following 3 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 1 1 0 1 1 1 0 0 1 0 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 0 1 0 ) acting on the columns of the generator matrix as follows (in order): (4, 8)(5, 15)(6, 9)(7, 14)(10, 19)(11, 16)(17, 18), (4, 15)(5, 9)(6, 8)(7, 14)(11, 21)(12, 18)(19, 20), (2, 3)(4, 5)(9, 15)(10, 16)(11, 20)(12, 18)(19, 21) orbits: { 1 }, { 2, 3 }, { 4, 8, 15, 5, 6, 9 }, { 7, 14 }, { 10, 19, 16, 20, 21, 11 }, { 12, 18, 17 }, { 13 } code no 12: ================ 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 1 the automorphism group has order 6 and is strongly generated by the following 2 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (5, 6, 14)(7, 9, 15)(10, 12, 19)(11, 16, 21)(17, 20, 18), (4, 8)(5, 15)(6, 9)(7, 14)(10, 19)(11, 16)(17, 18) orbits: { 1 }, { 2 }, { 3 }, { 4, 8 }, { 5, 14, 15, 6, 7, 9 }, { 10, 19, 12 }, { 11, 21, 16 }, { 13 }, { 17, 18, 20 } code no 13: ================ 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 1 the automorphism group has order 24 and is strongly generated by the following 4 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 0 0 1 0 0 1 0 1 0 1 1 0 0 1 , 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (4, 15)(5, 8)(6, 7)(9, 14)(10, 19)(11, 17)(16, 18), (4, 8)(5, 9)(6, 7)(10, 12)(14, 15)(16, 21)(17, 20), (2, 3)(5, 14)(8, 9)(10, 18)(11, 17)(12, 21)(16, 19), (1, 13)(2, 6)(3, 7)(4, 16, 5, 21, 14, 18)(8, 19, 15, 10, 9, 12)(11, 20, 17) orbits: { 1, 13 }, { 2, 3, 6, 7 }, { 4, 15, 8, 18, 14, 19, 5, 9, 12, 16, 10, 21 }, { 11, 17, 20 } code no 14: ================ 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 1 the automorphism group has order 96 and is strongly generated by the following 4 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 1 0 1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (4, 5)(6, 14)(7, 8)(9, 15)(11, 18)(12, 21)(19, 20), (3, 19, 20)(4, 16, 5)(6, 18, 15)(7, 8, 10)(9, 11, 14), (2, 19, 3)(4, 11, 15)(5, 6, 10)(7, 9, 16)(8, 18, 14), (2, 16, 5)(3, 18, 7)(6, 9, 8)(10, 14, 19)(11, 15, 20) orbits: { 1 }, { 2, 3, 5, 20, 19, 7, 4, 16, 10, 15, 14, 8, 18, 9, 6, 11 }, { 12, 21 }, { 13 }, { 17 } code no 15: ================ 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 the automorphism group has order 18 and is strongly generated by the following 4 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 0 1 1 1 0 1 0 1 0 , 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 ) acting on the columns of the generator matrix as follows (in order): (4, 8)(5, 7)(6, 15)(9, 14)(11, 20)(12, 18)(19, 21), (2, 19)(4, 11)(5, 7)(6, 16)(8, 18)(9, 10)(12, 20), (2, 18)(3, 5)(4, 19)(6, 15)(8, 11)(10, 14)(20, 21), (2, 18, 12)(3, 5, 7)(4, 11, 21)(8, 19, 20)(9, 10, 14) orbits: { 1 }, { 2, 19, 18, 12, 21, 4, 8, 20, 11 }, { 3, 5, 7 }, { 6, 15, 16 }, { 9, 14, 10 }, { 13 }, { 17 } code no 16: ================ 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 the automorphism group has order 288 and is strongly generated by the following 5 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 1 1 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 1 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 1 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 1 0 1 0 0 1 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (4, 6)(5, 14)(7, 9)(8, 15)(10, 16)(12, 20)(18, 19), (3, 19, 18)(4, 11, 6)(5, 15, 10)(7, 17, 9)(8, 14, 16), (3, 5, 14)(7, 9, 17)(8, 18, 10)(12, 20, 21)(15, 16, 19), (2, 4, 6)(3, 14, 5)(7, 8, 19)(9, 18, 15)(10, 16, 17), (2, 14)(3, 7)(4, 19)(5, 17)(6, 10)(8, 16)(9, 11)(15, 18) orbits: { 1 }, { 2, 6, 14, 4, 11, 10, 5, 8, 3, 19, 9, 16, 15, 18, 17, 7 }, { 12, 20, 21 }, { 13 } code no 17: ================ 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 the automorphism group has order 384 and is strongly generated by the following 6 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 1 0 0 0 1 1 1 0 1 0 1 0 1 1 0 1 0 1 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (12, 21), (7, 8)(9, 14)(10, 15)(11, 18)(16, 17)(19, 20), (4, 19, 5, 20)(6, 11, 13, 18)(7, 15, 9, 16)(8, 17, 14, 10), (4, 9)(5, 7)(6, 8)(10, 19)(11, 15)(13, 14)(16, 18)(17, 20), (2, 3)(4, 17, 20, 9)(5, 10, 19, 7)(6, 15, 18, 14)(8, 13, 16, 11), (1, 2, 3)(4, 11, 15, 13, 19, 16)(5, 20, 10, 6, 18, 17)(7, 9, 14) orbits: { 1, 3, 2 }, { 4, 20, 9, 16, 19, 5, 17, 14, 15, 7, 18, 13, 10, 8, 11, 6 }, { 12, 21 } code no 18: ================ 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 the automorphism group has order 72 and is strongly generated by the following 4 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 1 0 0 1 1 1 1 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 1 0 0 1 0 0 1 0 0 1 1 1 1 0 0 0 1 , 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (7, 10)(8, 15)(9, 16)(11, 12)(14, 17)(18, 20)(19, 21), (4, 7, 10)(5, 8, 15)(6, 9, 16)(11, 18, 19)(12, 21, 20)(13, 14, 17), (2, 3)(6, 13)(7, 10)(8, 15)(9, 17)(11, 18)(12, 20)(14, 16), (1, 7)(2, 10)(3, 4)(5, 14)(6, 17)(9, 15)(18, 19) orbits: { 1, 7, 10, 4, 2, 3 }, { 5, 15, 14, 8, 9, 17, 13, 16, 6 }, { 11, 12, 19, 18, 20, 21 } code no 19: ================ 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 the automorphism group has order 192 and is strongly generated by the following 5 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 1 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 1 0 0 0 1 , 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 1 1 1 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (4, 9)(5, 7)(6, 8)(10, 18)(11, 15)(13, 14)(16, 17), (3, 19)(4, 11)(5, 16)(7, 17)(9, 15)(12, 21)(13, 14), (2, 19)(4, 10)(5, 7)(9, 18)(12, 20)(13, 17)(14, 16), (1, 14)(2, 13)(3, 18)(4, 7)(5, 17)(9, 11)(10, 19)(15, 16), (1, 14, 15, 16)(2, 10, 7, 17)(3, 18, 11, 9)(4, 19, 13, 5)(12, 20) orbits: { 1, 14, 16, 13, 17, 5, 15, 2, 19, 7, 11, 9, 3, 10, 4, 18 }, { 6, 8 }, { 12, 21, 20 } code no 20: ================ 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 1 the automorphism group has order 3840 and is strongly generated by the following 9 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 0 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 1 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 0 0 0 1 1 ) acting on the columns of the generator matrix as follows (in order): (7, 9)(8, 14)(10, 11)(12, 17)(15, 16)(18, 20)(19, 21), (5, 13)(7, 9)(10, 19)(11, 21)(15, 18)(16, 20), (4, 8)(5, 7)(6, 14)(9, 13)(10, 15)(18, 19), (4, 13)(5, 6)(7, 14)(8, 9)(10, 15)(11, 16)(12, 17), (4, 7)(5, 8)(6, 9)(10, 15)(12, 17)(13, 14)(20, 21), (4, 19)(5, 20)(6, 18)(7, 11)(8, 15)(9, 16)(10, 14)(13, 21), (3, 17)(4, 19)(5, 7)(6, 15)(8, 18)(10, 14)(11, 20), (2, 7, 19, 14)(3, 13, 18, 4)(5, 10, 8, 17)(6, 12, 9, 15)(11, 16), (2, 21)(3, 16, 17, 20, 12, 11)(4, 19, 13)(5, 6, 15, 7, 14, 10)(8, 18, 9) orbits: { 1 }, { 2, 14, 21, 8, 6, 7, 13, 10, 19, 11, 20, 4, 9, 5, 15, 18, 3, 16, 12, 17 }