the 7 isometry classes of irreducible [21,17,4]_5 codes are: code no 1: ================ 1 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 3 2 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 4 4 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 3 0 1 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 4 3 1 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 4 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 2 0 2 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 3 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 2 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 1 0 0 0 0 1 0 0 1 2 3 3 2 4 4 2 , 0 2 0 0 3 0 0 0 4 3 4 0 0 0 0 4 ) acting on the columns of the generator matrix as follows (in order): (3, 14)(4, 16)(5, 6)(7, 13)(8, 12)(9, 15)(10, 17)(11, 18), (1, 2)(3, 7)(5, 12)(6, 8)(10, 11)(13, 14)(17, 18)(20, 21) orbits: { 1, 2 }, { 3, 14, 7, 13 }, { 4, 16 }, { 5, 6, 12, 8 }, { 9, 15 }, { 10, 17, 11, 18 }, { 19 }, { 20, 21 } code no 2: ================ 1 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 3 2 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 4 4 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 3 0 1 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 4 3 1 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 4 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 2 0 2 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 3 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 4 and is strongly generated by the following 1 elements: ( 3 0 1 1 1 1 2 0 0 2 1 2 1 2 1 0 ) acting on the columns of the generator matrix as follows (in order): (1, 8, 2, 12)(3, 20, 14, 19)(4, 5, 17, 7)(6, 16, 13, 10)(9, 15, 18, 11) orbits: { 1, 12, 2, 8 }, { 3, 19, 14, 20 }, { 4, 7, 17, 5 }, { 6, 10, 13, 16 }, { 9, 11, 18, 15 }, { 21 } code no 3: ================ 1 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 3 2 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 4 4 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 3 0 1 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 4 3 1 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 4 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 2 0 2 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 3 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 1 4 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 2 0 0 0 0 2 0 0 2 0 4 4 2 0 2 1 ) acting on the columns of the generator matrix as follows (in order): (3, 12)(4, 15)(5, 7)(6, 13)(8, 14)(9, 16)(10, 18)(11, 17)(19, 20) orbits: { 1 }, { 2 }, { 3, 12 }, { 4, 15 }, { 5, 7 }, { 6, 13 }, { 8, 14 }, { 9, 16 }, { 10, 18 }, { 11, 17 }, { 19, 20 }, { 21 } code no 4: ================ 1 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 3 2 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 4 4 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 3 0 1 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 4 3 1 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 4 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 2 0 2 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 2 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 4 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 0 4 0 0 1 0 0 0 4 2 2 0 4 2 0 2 ) acting on the columns of the generator matrix as follows (in order): (1, 2)(3, 6)(4, 9)(5, 14)(7, 8)(12, 13)(15, 16)(18, 21) orbits: { 1, 2 }, { 3, 6 }, { 4, 9 }, { 5, 14 }, { 7, 8 }, { 10 }, { 11 }, { 12, 13 }, { 15, 16 }, { 17 }, { 18, 21 }, { 19 }, { 20 } code no 5: ================ 1 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 3 2 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 4 4 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 3 0 1 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 4 3 1 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 4 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 2 0 2 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 2 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 4 3 1 1 3 4 1 2 2 3 3 1 2 3 0 4 ) acting on the columns of the generator matrix as follows (in order): (1, 13)(2, 19)(3, 20)(4, 10)(5, 9)(6, 8)(7, 14)(11, 18)(12, 15)(16, 21) orbits: { 1, 13 }, { 2, 19 }, { 3, 20 }, { 4, 10 }, { 5, 9 }, { 6, 8 }, { 7, 14 }, { 11, 18 }, { 12, 15 }, { 16, 21 }, { 17 } code no 6: ================ 1 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 3 2 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 4 4 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 3 0 1 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 4 3 1 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 4 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 2 0 2 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 4 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 3 3 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 12 and is strongly generated by the following 2 elements: ( 2 0 0 0 4 1 0 3 4 4 2 3 1 1 0 4 , 0 0 0 4 1 1 0 4 3 3 3 3 4 1 0 3 ) acting on the columns of the generator matrix as follows (in order): (2, 10)(3, 21)(4, 11)(5, 8)(6, 15)(7, 19)(13, 17)(14, 18)(16, 20), (1, 11, 2, 9, 10, 4)(3, 7, 20, 18, 15, 5)(6, 14, 16, 19, 21, 8)(12, 17, 13) orbits: { 1, 4, 11, 10, 2, 9 }, { 3, 21, 5, 19, 8, 15, 7, 16, 6, 18, 20, 14 }, { 12, 13, 17 } code no 7: ================ 1 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 3 2 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 4 4 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 3 0 1 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 4 3 1 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 2 4 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 2 0 2 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 4 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 2 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 3 3 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 40 and is strongly generated by the following 3 elements: ( 3 0 0 0 0 0 0 4 0 2 3 4 0 1 0 0 , 4 3 4 0 4 4 2 3 1 2 2 1 2 1 4 3 , 0 2 3 4 3 1 4 4 3 1 3 0 3 3 3 3 ) acting on the columns of the generator matrix as follows (in order): (2, 4)(3, 17)(6, 14)(7, 20)(8, 18)(9, 11)(12, 16)(13, 19), (1, 20, 9, 18, 4, 21, 2, 8, 11, 7)(3, 19, 6, 15, 14, 13, 17, 12, 5, 16), (1, 12, 8, 17)(2, 16, 20, 14)(3, 11, 15, 7)(4, 13, 18, 5)(6, 9, 19, 21) orbits: { 1, 7, 17, 20, 11, 15, 3, 13, 8, 16, 9, 6, 19, 14, 4, 18, 2, 12, 5, 21 }, { 10 }