the 27 isometry classes of irreducible [21,4,10]_2 codes are: code no 1: ================ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 the automorphism group has order 27648 and is strongly generated by the following 12 elements: ( 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 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 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 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 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 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 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 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 1 1 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 1 0 1 1 0 0 1 1 0 0 0 0 0 1 the automorphism group has order 20736 and is strongly generated by the following 12 elements: ( 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 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 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 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 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 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 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 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 1 1 1 1 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 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 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 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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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 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 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 ) acting on the columns of the generator matrix as follows (in order): (17, 18), (16, 18), (14, 15)(16, 18, 17), (12, 13)(14, 15)(16, 17), (10, 11)(14, 15)(17, 18), (7, 8)(12, 13)(16, 17), (6, 7, 8)(10, 11)(17, 18), (4, 5), (3, 5)(6, 8)(16, 17, 18), (3, 7, 4, 8)(5, 6)(12, 15)(13, 14)(17, 18)(20, 21), (1, 14, 2, 15)(3, 18)(4, 17, 5, 16)(6, 8, 7)(10, 11)(19, 20), (1, 15, 13, 2, 14, 12)(3, 7, 17, 4, 6, 16, 5, 8, 18)(19, 20, 21) orbits: { 1, 15, 12, 14, 2, 13 }, { 3, 5, 8, 18, 4, 6, 17, 16, 7 }, { 9 }, { 10, 11 }, { 19, 20, 21 } code no 3: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 1 the automorphism group has order 497664 and is strongly generated by the following 16 elements: ( 1 0 0 0 0 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0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 1 0 1 0 1 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1 the automorphism group has order 20736 and is strongly generated by the following 13 elements: ( 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 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 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 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 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 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 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 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 1 0 1 0 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 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 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 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 0 0 0 0 0 0 0 0 1 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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 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 , 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 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 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 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 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 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 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 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 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ) acting on the columns of the generator matrix as follows (in order): (17, 21), (16, 17), (16, 21), (15, 20), (14, 20, 15), (13, 19)(14, 20, 15), (12, 13, 19)(14, 15), (10, 11)(12, 19, 13)(14, 15, 20), (9, 18)(10, 11)(12, 13, 19), (4, 6)(5, 7)(9, 18)(10, 11)(12, 20, 13, 15)(14, 19)(16, 17), (3, 6)(5, 8)(9, 18)(10, 11)(12, 17, 19, 16, 13, 21)(14, 15), (1, 2)(9, 18)(16, 17), (1, 18)(2, 9)(3, 8)(4, 7)(5, 6)(10, 11)(13, 19)(14, 15, 20)(16, 17) orbits: { 1, 2, 18, 9 }, { 3, 6, 8, 4, 5, 7 }, { 10, 11 }, { 12, 19, 13, 15, 21, 14, 17, 20, 16 } code no 5: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 the automorphism group has order 3456 and is strongly generated by the following 11 elements: ( 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 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 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 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 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 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 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 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 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 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 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 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 , 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 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 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 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 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 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 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 0 1 0 0 0 0 0 0 0 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 1 1 1 0 0 1 1 0 0 1 1 0 0 1 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 0 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (17, 21), (16, 17), (16, 21), (15, 20)(16, 17), (14, 20), (14, 20, 15), (13, 19)(15, 20)(16, 17), (9, 18)(13, 19)(14, 15)(16, 17), (6, 10)(7, 11)(8, 12)(9, 19, 18, 13)(16, 17), (3, 4)(6, 10)(7, 12)(8, 11)(9, 13, 18, 19)(14, 21)(15, 16, 20, 17), (1, 19, 9, 2, 13, 18)(3, 12, 8)(4, 11, 7)(5, 10, 6)(14, 20, 15) orbits: { 1, 18, 9, 19, 13, 2 }, { 3, 4, 8, 7, 12, 11 }, { 5, 6, 10 }, { 14, 20, 15, 21, 16, 17 } code no 6: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 0 0 1 1 1 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 the automorphism group has order 2304 and is strongly generated by the following 11 elements: ( 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 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 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 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 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 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1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 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): (17, 21), (16, 17), (16, 21), (15, 20), (14, 20, 15), (13, 19)(14, 15, 20), (9, 18)(13, 19)(14, 20, 15), (6, 10)(7, 11)(8, 12)(9, 19, 18, 13)(14, 15, 20)(16, 17), (4, 5)(6, 10)(7, 11)(8, 12)(9, 13)(14, 15, 20)(16, 17)(18, 19), (2, 3)(6, 10)(7, 11)(8, 12)(9, 19)(13, 18)(14, 20)(16, 17), (2, 4)(3, 5)(7, 8)(9, 18)(11, 12)(14, 17, 20, 16, 15, 21) orbits: { 1 }, { 2, 3, 4, 5 }, { 6, 10 }, { 7, 11, 8, 12 }, { 9, 18, 13, 19 }, { 14, 15, 20, 21, 16, 17 } code no 7: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 1 1 0 0 0 1 the automorphism group has order 4608 and is strongly generated by the following 11 elements: ( 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 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 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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 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 1 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 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 ) acting on the columns of the generator matrix as follows (in order): (17, 21), (16, 17), (16, 21), (15, 20)(16, 17), (14, 20, 15), (13, 19)(15, 20)(16, 17), (9, 18)(13, 19)(16, 17), (6, 7)(9, 18)(14, 15, 20), (4, 5)(9, 18)(13, 19)(14, 15), (1, 9)(2, 18)(3, 8)(4, 7)(5, 6)(13, 19)(16, 17), (1, 4)(2, 5)(6, 9, 7, 18)(11, 12)(13, 19)(14, 16, 15, 21)(17, 20) orbits: { 1, 9, 4, 18, 6, 5, 7, 2 }, { 3, 8 }, { 10 }, { 11, 12 }, { 13, 19 }, { 14, 15, 20, 21, 16, 17 } code no 8: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 0 0 0 1 the automorphism group has order 4608 and is strongly generated by the following 12 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generator matrix as follows (in order): (17, 21), (16, 17), (16, 17, 21), (15, 20), (13, 19), (10, 11)(13, 19)(16, 17), (9, 18)(10, 11)(13, 19)(15, 20), (6, 7)(9, 18)(13, 19)(15, 20), (6, 11)(7, 10)(8, 12)(9, 19, 18, 13)(15, 20)(16, 17), (4, 5)(6, 7)(9, 18)(13, 19)(16, 17), (1, 9, 2, 18)(3, 8)(4, 6, 5, 7)(13, 19)(15, 20), (1, 13, 2, 19)(3, 12)(4, 10, 5, 11)(6, 7) orbits: { 1, 18, 19, 9, 2, 13 }, { 3, 8, 12 }, { 4, 5, 7, 11, 6, 10 }, { 14 }, { 15, 20 }, { 16, 17, 21 } code no 9: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 1 0 1 0 1 0 1 0 0 0 1 0 1 0 1 1 0 0 0 1 the automorphism group has order 768 and is strongly generated by the following 10 elements: ( 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 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 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 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 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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 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 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 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 0 1 0 0 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 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 1 1 1 1 1 0 0 0 0 1 1 1 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 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 0 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (17, 21), (16, 17), (16, 17, 21), (15, 20)(16, 17), (13, 19)(16, 17), (10, 11)(13, 19)(15, 20), (9, 18), (4, 6)(5, 7)(9, 18)(12, 14)(13, 20, 19, 15), (1, 2)(9, 18)(10, 11)(13, 19)(15, 20)(16, 17), (1, 18)(2, 9)(3, 8)(4, 7)(5, 6)(13, 19) orbits: { 1, 2, 18, 9 }, { 3, 8 }, { 4, 6, 7, 5 }, { 10, 11 }, { 12, 14 }, { 13, 19, 15, 20 }, { 16, 17, 21 } code no 10: 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19) orbits: { 1, 8, 14, 12 }, { 2, 3, 9, 20, 18, 15, 13, 19 }, { 4, 5 }, { 6 }, { 7 }, { 10, 11 }, { 16, 17, 21 } code no 11: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 0 0 1 the automorphism group has order 2304 and is strongly generated by the following 10 elements: ( 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 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 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 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 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 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 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 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 1 0 1 0 1 0 1 0 1 0 1 0 1 1 , 1 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 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 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 0 0 0 0 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (17, 21), (16, 17), (16, 21), (15, 20)(16, 17), (13, 19)(15, 20)(16, 17), (9, 18)(13, 19)(16, 17), (6, 10)(7, 11)(8, 12)(9, 13)(15, 20)(16, 17)(18, 19), (4, 6, 10)(5, 7, 11)(8, 14, 12)(9, 20, 19)(13, 18, 15), (2, 3)(4, 10, 6)(5, 11, 7)(8, 12, 14)(9, 19, 20)(13, 15, 18)(16, 17), (1, 14, 8)(2, 15, 18)(3, 20, 9)(4, 6, 10)(5, 7, 11)(13, 19) orbits: { 1, 8, 12, 14 }, { 2, 3, 18, 9, 19, 13, 15, 20 }, { 4, 10, 6 }, { 5, 11, 7 }, { 16, 17, 21 } code no 12: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 0 0 1 the automorphism group has order 2304 and is strongly generated by the following 10 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13)(16, 17)(18, 19), (4, 10)(5, 11)(8, 14)(9, 20)(13, 19)(15, 18)(16, 17), (1, 20)(2, 15)(3, 14)(6, 11)(7, 10)(9, 18)(13, 19)(16, 17), (1, 9, 13, 2, 18, 19)(3, 8, 12)(4, 7, 11)(5, 6, 10)(16, 17) orbits: { 1, 20, 19, 15, 9, 13, 18, 2 }, { 3, 14, 12, 8 }, { 4, 10, 11, 6, 7, 5 }, { 16, 17, 21 } code no 13: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 1 0 0 0 1 the automorphism group has order 1536 and is strongly generated by the following 11 elements: ( 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 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 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 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 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 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 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generator matrix as follows (in order): (17, 21), (16, 17), (16, 17, 21), (15, 20)(16, 17), (13, 19)(15, 20)(16, 17), (9, 18)(16, 17), (6, 10)(7, 11)(8, 12)(9, 19)(13, 18), (4, 5)(6, 10)(7, 11)(8, 12)(9, 19, 18, 13), (2, 3)(9, 18)(13, 19)(15, 20), (1, 12)(2, 19, 3, 13)(8, 14)(9, 20, 18, 15), (1, 14)(2, 15, 3, 20)(6, 10)(7, 11)(9, 18) orbits: { 1, 12, 14, 8 }, { 2, 3, 13, 20, 19, 15, 18, 9 }, { 4, 5 }, { 6, 10 }, { 7, 11 }, { 16, 17, 21 } code no 14: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 1 1 0 0 0 1 the automorphism group has order 3072 and is strongly generated by the following 11 elements: ( 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 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 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 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 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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 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 ) acting on the columns of the generator matrix as follows (in order): (17, 21), (16, 17), (16, 21), (15, 20), (13, 19), (9, 18)(15, 20), (6, 7)(13, 19), (4, 5)(9, 18), (4, 6, 5, 7)(9, 18)(12, 14)(13, 20, 19, 15)(16, 17), (2, 3)(16, 17), (1, 12)(2, 19)(3, 13)(4, 5)(8, 14)(9, 15)(16, 17)(18, 20) orbits: { 1, 12, 14, 8 }, { 2, 3, 19, 13, 20, 15, 18, 9 }, { 4, 5, 7, 6 }, { 10 }, { 11 }, { 16, 17, 21 } code no 15: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 1 0 1 1 1 0 1 0 1 1 0 0 0 1 the automorphism group has order 18432 and is strongly generated by the following 12 elements: ( 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 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 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 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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 0 0 1 0 0 0 0 0 0 0 0 0 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 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 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 1 1 1 1 0 0 0 0 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 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 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 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 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 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 0 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 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 0 0 0 1 0 ) acting on the columns of the generator matrix as follows (in order): (17, 21), (16, 17), (16, 21), (15, 20)(16, 17), (13, 19)(15, 20), (10, 11)(13, 19)(16, 17), (9, 18)(13, 19)(16, 17), (6, 10)(7, 11)(8, 12)(9, 13)(15, 20)(16, 17)(18, 19), (4, 10)(5, 11)(6, 7)(8, 14)(9, 20, 18, 15), (2, 3)(4, 5)(15, 20)(16, 17), (1, 8, 14)(2, 18, 15, 3, 9, 20)(4, 10, 7, 5, 11, 6), (1, 8, 12)(2, 9, 19, 3, 18, 13)(4, 7, 10)(5, 6, 11)(15, 20)(16, 17) orbits: { 1, 14, 12, 8 }, { 2, 3, 20, 13, 15, 19, 9, 18 }, { 4, 10, 5, 6, 11, 7 }, { 16, 17, 21 } code no 16: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 0 0 1 the automorphism group has order 24576 and is strongly generated by the following 12 elements: ( 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 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 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 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 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 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 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2, 20)(3, 14, 4, 15)(6, 10)(7, 18)(8, 9)(11, 13, 12, 19) orbits: { 1, 7, 20, 8, 12, 11, 14, 2, 18, 16, 13, 15, 9, 19, 3, 4 }, { 5, 10, 6 }, { 17, 21 } code no 17: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 1 0 1 0 0 0 1 the automorphism group has order 24576 and is strongly generated by the following 13 elements: ( 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 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 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 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 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 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 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 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 1 0 0 1 0 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columns of the generator matrix as follows (in order): (17, 21), (16, 20), (14, 15), (13, 19), (11, 12)(14, 15), (9, 18)(11, 12)(13, 19)(14, 15), (7, 8), (6, 10)(7, 12)(8, 11)(9, 19)(13, 18)(14, 15)(16, 20), (5, 10)(7, 20, 8, 16)(9, 14)(11, 12)(13, 19)(15, 18), (5, 6)(7, 8)(9, 18)(11, 20, 12, 16)(13, 15)(14, 19), (3, 4)(14, 15), (1, 9, 13, 2, 18, 19)(3, 7, 12, 4, 8, 11)(5, 6, 10), (1, 12, 2, 11)(3, 13)(4, 19)(7, 15, 8, 14)(9, 16, 18, 20) orbits: { 1, 19, 11, 13, 9, 14, 18, 4, 12, 8, 16, 2, 15, 3, 20, 7 }, { 5, 10, 6 }, { 17, 21 } code no 18: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 the automorphism group has order 2048 and is strongly generated by the following 10 elements: ( 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 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 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 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20) orbits: { 1, 9, 14, 18, 13, 15, 19, 2 }, { 3, 4, 8, 10 }, { 5 }, { 6, 7, 12, 21, 11, 17, 20, 16 } code no 19: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 the automorphism group has order 18432 and is strongly generated by the following 12 elements: ( 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 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 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 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 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 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 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 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 1 1 0 0 1 0 0 1 1 0 1 1 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 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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): (17, 21), (16, 20), (14, 15), (13, 19), (11, 12), (9, 18)(13, 19)(16, 20), (4, 6)(5, 7)(11, 15, 12, 14)(13, 20)(16, 19), (4, 5)(6, 7)(11, 19)(12, 13)(14, 20, 15, 16), (2, 3), (1, 8)(2, 9, 3, 18)(4, 6)(5, 7)(13, 19) orbits: { 1, 8 }, { 2, 3, 18, 9 }, { 4, 6, 5, 7 }, { 10 }, { 11, 12, 14, 19, 15, 13, 16, 20 }, { 17, 21 } code no 21: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 the automorphism group has order 1024 and is strongly generated by the following 9 elements: ( 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 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 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 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 0 0 0 0 0 0 0 0 1 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(17, 21), (16, 20), (14, 15), (13, 19)(14, 15)(16, 20), (11, 12)(13, 19)(14, 15), (9, 18)(14, 15), (4, 7)(5, 6)(11, 20)(12, 16)(13, 14, 19, 15), (4, 5)(6, 7)(11, 19, 12, 13)(14, 20)(15, 16), (1, 9)(2, 18)(3, 8)(4, 7)(5, 6)(13, 19) orbits: { 1, 9, 18, 2 }, { 3, 8 }, { 4, 7, 5, 6 }, { 10 }, { 11, 12, 20, 13, 16, 19, 14, 15 }, { 17, 21 } code no 22: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 the automorphism group has order 4608 and is strongly generated by the following 11 elements: ( 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 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 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 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 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 0 0 0 0 0 0 0 0 1 0 0 0 0 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0 0 1 0 ) acting on the columns of the generator matrix as follows (in order): (17, 21), (16, 20), (14, 15), (13, 19), (9, 18)(14, 15), (6, 10)(7, 11)(8, 12)(9, 13, 18, 19)(16, 20), (4, 5)(6, 10)(7, 11)(8, 12)(9, 19, 18, 13), (2, 10, 3, 6)(4, 14)(5, 15)(7, 11, 12, 8)(9, 16, 19, 21, 18, 20, 13, 17), (1, 6, 10)(2, 7, 11)(3, 8, 12)(4, 9, 13, 5, 18, 19), (1, 7, 10, 2, 6, 11)(3, 8, 12)(4, 9, 13, 5, 18, 19)(14, 20, 15, 16), (1, 2, 3)(4, 5)(6, 7, 8)(9, 18)(10, 11, 12)(13, 19)(14, 16, 17, 15, 20, 21) orbits: { 1, 10, 11, 3, 6, 2, 7, 12, 8 }, { 4, 5, 14, 19, 15, 13, 16, 21, 18, 9, 20, 17 } code no 23: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 the automorphism group has order 768 and is strongly generated by the following 10 elements: ( 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 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 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6)(3, 19, 9, 4, 13, 18)(5, 12, 8)(14, 15) orbits: { 1, 11, 2, 7, 10, 6 }, { 3, 4, 13, 18, 19, 9 }, { 5, 12, 8 }, { 14, 15, 20, 16 }, { 17, 21 } code no 24: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 1 1 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 0 0 0 1 the automorphism group has order 3072 and is strongly generated by the following 8 elements: ( 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 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 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 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 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 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 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 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 1 1 0 1 1 0 1 0 1 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0 0 0 1 1 1 1 0 0 0 0 0 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 ) acting on the columns of the generator matrix as follows (in order): (17, 21), (16, 20), (14, 19), (10, 11)(14, 19), (9, 18)(10, 11)(16, 20), (5, 19)(6, 14)(7, 13)(8, 12)(9, 10)(11, 18), (5, 11, 6, 10)(7, 12)(8, 13)(9, 14, 18, 19)(16, 20), (2, 10, 5)(3, 11, 6)(4, 12, 7)(8, 13, 15)(9, 14, 20, 18, 19, 16) orbits: { 1 }, { 2, 5, 19, 10, 14, 18, 11, 9, 6, 20, 3, 16 }, { 4, 7, 13, 12, 8, 15 }, { 17, 21 } code no 25: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 1 1 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 0 0 0 1 the automorphism group has order 21504 and is strongly generated by the following 9 elements: ( 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 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 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 0 0 0 0 0 0 0 0 1 0 0 0 0 0 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on the columns of the generator matrix as follows (in order): (17, 21), (16, 20), (14, 19), (10, 11)(16, 20), (9, 18)(16, 20), (5, 18)(6, 9)(7, 8)(10, 19)(11, 14)(12, 13), (5, 10, 6, 11)(7, 12)(8, 13)(9, 19)(14, 18), (2, 18, 19)(3, 9, 14)(4, 8, 13)(5, 20, 11)(6, 16, 10)(7, 15, 12), (1, 15, 4)(2, 16, 17, 3, 20, 21)(5, 19, 11, 6, 14, 10)(7, 8, 13)(9, 18) orbits: { 1, 4, 13, 15, 12, 8, 7 }, { 2, 19, 21, 14, 10, 9, 18, 5, 17, 20, 11, 6, 16, 3 } code no 26: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 0 0 0 1 the automorphism group has order 3072 and is strongly generated by the following 10 elements: ( 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 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 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 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 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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 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 0 1 1 0 1 0 1 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 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 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 0 1 1 1 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 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 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 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (17, 21), (16, 20), (14, 19), (10, 11)(14, 19), (9, 18)(14, 19), (5, 14)(6, 19)(7, 13)(8, 12)(9, 10, 18, 11), (5, 9, 6, 18)(7, 8)(10, 19)(11, 14)(12, 13), (2, 3)(5, 9, 6, 18)(10, 14)(11, 19)(16, 21, 20, 17), (1, 4)(2, 3)(5, 14, 9, 10, 6, 19, 18, 11)(7, 13, 8, 12), (1, 13, 4, 12)(5, 16, 9, 21)(6, 20, 18, 17)(7, 8)(10, 14, 11, 19) orbits: { 1, 4, 12, 13, 8, 7 }, { 2, 3 }, { 5, 14, 18, 11, 21, 19, 10, 9, 6, 20, 17, 16 }, { 15 } code no 27: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 0 1 0 0 0 1 the automorphism group has order 16384 and is strongly generated by the following 13 elements: ( 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 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 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 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 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 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 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 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 1 0 1 0 1 1 0 1 0 1 0 1 , 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 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 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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 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 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 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 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 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 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 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 0 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 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 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 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1 1 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 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (17, 21), (16, 20), (14, 19)(16, 20), (10, 11)(14, 19)(16, 20), (9, 18), (7, 8)(10, 14, 11, 19)(16, 21, 20, 17), (5, 6), (5, 19)(6, 14)(7, 13)(8, 12)(9, 10, 18, 11), (5, 11)(6, 10)(7, 12)(8, 13)(9, 14)(18, 19), (3, 4)(5, 19)(6, 14)(7, 13)(8, 12)(9, 11, 18, 10), (1, 4)(2, 3)(9, 18)(10, 19, 11, 14)(12, 13), (1, 16, 3, 21)(2, 20, 4, 17)(5, 11, 9, 14, 6, 10, 18, 19)(7, 8), (1, 18, 4, 6, 2, 9, 3, 5)(7, 8)(10, 16, 19, 17, 11, 20, 14, 21)(12, 13) orbits: { 1, 4, 21, 5, 3, 20, 18, 17, 16, 14, 6, 19, 11, 2, 9, 10 }, { 7, 8, 13, 12 }, { 15 }