the 38 isometry classes of irreducible [8,3,4]_4 codes are: code no 1: ================ 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 3 2 1 0 0 0 0 1 the automorphism group has order 144 and is strongly generated by the following 8 elements: ( 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 0 3 3 3 3 3 , 0 , 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 3 3 3 3 3 0 0 0 0 3 , 0 , 2 0 0 0 0 0 1 0 0 0 1 2 3 0 0 3 3 3 3 3 0 0 0 3 0 , 1 , 3 0 0 0 0 0 0 3 0 0 0 3 0 0 0 3 3 3 3 3 0 0 0 0 3 , 1 , 3 0 0 0 0 1 2 3 0 0 0 0 1 0 0 2 2 2 2 2 0 0 0 0 2 , 1 , 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 , 1 , 0 3 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 3 0 3 3 3 3 3 , 1 , 3 1 2 0 0 0 0 3 0 0 2 0 0 0 0 0 0 0 1 0 0 0 0 0 1 , 1 ) acting on the columns of the generator matrix as follows (in order): (5, 6), (4, 6), (3, 8)(4, 5, 6), (2, 3)(4, 6), (2, 8)(4, 6), (1, 3), (1, 2)(5, 6), (1, 3, 2, 8) orbits: { 1, 3, 2, 8 }, { 4, 6, 5 }, { 7 } code no 2: ================ 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 1 1 0 1 0 0 0 1 the automorphism group has order 64 and is strongly generated by the following 5 elements: ( 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 , 1 , 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 2 2 2 2 2 , 1 , 2 0 0 0 0 0 2 0 0 0 2 2 0 2 0 2 2 2 0 0 0 0 0 0 2 , 0 , 2 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 2 0 0 2 2 2 2 2 , 1 , 3 3 3 3 3 0 0 0 0 3 0 0 0 3 0 0 0 3 0 0 0 3 0 0 0 , 1 ) acting on the columns of the generator matrix as follows (in order): id, (5, 6), (3, 8)(4, 7), (3, 4)(5, 6)(7, 8), (1, 6)(2, 5)(3, 4) orbits: { 1, 6, 5, 2 }, { 3, 8, 4, 7 } code no 3: ================ 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 2 1 0 1 0 0 0 1 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 2 2 2 2 2 , 0 , 1 0 0 0 0 0 2 0 0 0 1 2 0 2 0 2 2 2 0 0 2 2 2 2 2 , 1 ) acting on the columns of the generator matrix as follows (in order): (5, 6), (3, 8)(4, 7)(5, 6) orbits: { 1 }, { 2 }, { 3, 8 }, { 4, 7 }, { 5, 6 } code no 4: ================ 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 2 2 0 1 0 0 0 1 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 0 3 3 3 3 3 , 0 , 2 0 0 0 0 0 2 0 0 0 2 2 0 3 0 3 3 3 0 0 0 0 0 0 3 , 1 , 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 , 0 ) acting on the columns of the generator matrix as follows (in order): (5, 6), (3, 8)(4, 7), (1, 2) orbits: { 1, 2 }, { 3, 8 }, { 4, 7 }, { 5, 6 } code no 5: ================ 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 3 2 0 1 0 0 0 1 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 2 2 2 2 2 , 0 , 1 0 0 0 0 0 2 0 0 0 1 2 0 3 0 3 3 3 0 0 3 3 3 3 3 , 1 , 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 , 1 ) acting on the columns of the generator matrix as follows (in order): (5, 6), (3, 8)(4, 7)(5, 6), (1, 2) orbits: { 1, 2 }, { 3, 8 }, { 4, 7 }, { 5, 6 } code no 6: ================ 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 2 2 1 1 0 0 0 1 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 1 , 0 , 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 1 , 0 , 2 2 2 2 2 0 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 , 1 ) acting on the columns of the generator matrix as follows (in order): (5, 6), (1, 2)(5, 6), (1, 6)(2, 5)(3, 4) orbits: { 1, 2, 6, 5 }, { 3, 4 }, { 7 }, { 8 } code no 7: ================ 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 3 2 1 1 0 0 0 1 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 0 3 3 3 3 3 , 0 , 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 , 1 ) acting on the columns of the generator matrix as follows (in order): (5, 6), (1, 2) orbits: { 1, 2 }, { 3 }, { 4 }, { 5, 6 }, { 7 }, { 8 } code no 8: ================ 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 3 2 2 1 0 0 0 1 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 2 2 2 2 2 , 0 , 2 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 2 0 2 2 2 2 2 , 0 , 0 0 0 2 0 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 0 2 0 0 0 , 0 ) acting on the columns of the generator matrix as follows (in order): (5, 6), (2, 3)(5, 6), (1, 4)(2, 5)(3, 6) orbits: { 1, 4 }, { 2, 3, 5, 6 }, { 7 }, { 8 } code no 9: ================ 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 2 1 0 2 1 0 0 1 the automorphism group has order 12 and is strongly generated by the following 3 elements: ( 3 0 0 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 3 0 3 3 3 3 3 , 1 , 0 3 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 3 0 , 1 , 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 0 0 0 0 , 1 ) acting on the columns of the generator matrix as follows (in order): (2, 3)(5, 6), (1, 2)(4, 5), (1, 5)(2, 4)(3, 6) orbits: { 1, 2, 5, 3, 4, 6 }, { 7 }, { 8 } code no 10: ================ 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 3 1 0 2 1 0 0 1 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 3 0 0 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 3 0 3 3 3 3 3 , 1 , 0 0 0 2 0 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 0 2 0 0 0 , 1 ) acting on the columns of the generator matrix as follows (in order): (2, 3)(5, 6), (1, 4)(2, 5)(3, 6) orbits: { 1, 4 }, { 2, 3, 5, 6 }, { 7 }, { 8 } code no 11: ================ 1 1 1 1 1 1 0 0 2 1 1 0 0 0 1 0 1 2 1 0 0 0 0 1 the automorphism group has order 48 and is strongly generated by the following 5 elements: ( 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 2 2 2 2 2 , 0 , 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 3 3 3 3 3 0 0 0 0 3 , 0 , 1 0 0 0 0 3 2 3 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 2 , 1 , 2 3 3 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 2 2 2 2 2 2 , 1 , 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 , 0 ) acting on the columns of the generator matrix as follows (in order): (5, 6), (4, 6), (2, 8), (1, 7)(4, 6, 5), (1, 2)(4, 5)(7, 8) orbits: { 1, 7, 2, 8 }, { 3 }, { 4, 6, 5 } code no 12: ================ 1 1 1 1 1 1 0 0 2 1 1 0 0 0 1 0 2 1 0 1 0 0 0 1 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 0 3 3 3 3 3 , 0 , 1 0 0 0 0 0 1 0 0 0 2 1 1 0 0 2 1 0 1 0 0 0 0 0 1 , 0 , 3 0 0 0 0 0 3 0 0 0 1 3 0 3 0 1 3 3 0 0 3 3 3 3 3 , 0 ) acting on the columns of the generator matrix as follows (in order): (5, 6), (3, 7)(4, 8), (3, 8)(4, 7)(5, 6) orbits: { 1 }, { 2 }, { 3, 7, 8, 4 }, { 5, 6 } code no 13: ================ 1 1 1 1 1 1 0 0 2 1 1 0 0 0 1 0 3 1 0 1 0 0 0 1 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 2 2 2 2 2 , 0 , 3 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 3 0 0 3 3 3 3 3 , 1 ) acting on the columns of the generator matrix as follows (in order): (5, 6), (3, 4)(5, 6)(7, 8) orbits: { 1 }, { 2 }, { 3, 4 }, { 5, 6 }, { 7, 8 } code no 14: ================ 1 1 1 1 1 1 0 0 2 1 1 0 0 0 1 0 1 2 0 1 0 0 0 1 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 2 2 2 2 2 , 0 , 3 0 0 0 0 0 3 0 0 0 1 3 0 1 0 3 1 1 0 0 0 0 0 0 1 , 1 , 0 2 0 0 0 2 0 0 0 0 2 3 3 0 0 3 2 0 3 0 0 0 0 0 3 , 1 ) acting on the columns of the generator matrix as follows (in order): (5, 6), (3, 8)(4, 7), (1, 2)(3, 7)(4, 8) orbits: { 1, 2 }, { 3, 8, 7, 4 }, { 5, 6 } code no 15: ================ 1 1 1 1 1 1 0 0 2 1 1 0 0 0 1 0 2 2 0 1 0 0 0 1 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 0 3 3 3 3 3 , 0 ) acting on the columns of the generator matrix as follows (in order): (5, 6) orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5, 6 }, { 7 }, { 8 } code no 16: ================ 1 1 1 1 1 1 0 0 2 1 1 0 0 0 1 0 1 3 0 1 0 0 0 1 the automorphism group has order 24 and is strongly generated by the following 4 elements: ( 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 0 3 3 3 3 3 , 0 , 1 0 0 0 0 0 3 0 0 0 2 3 0 2 0 1 2 2 0 0 2 2 2 2 2 , 1 , 1 2 2 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 1 0 0 0 0 0 1 , 1 , 2 1 0 2 0 0 0 0 3 0 3 0 0 0 0 0 0 1 0 0 1 1 1 1 1 , 0 ) acting on the columns of the generator matrix as follows (in order): (5, 6), (3, 8)(4, 7)(5, 6), (1, 7)(2, 3), (1, 3, 4, 2, 7, 8)(5, 6) orbits: { 1, 7, 8, 4, 2, 3 }, { 5, 6 } code no 17: ================ 1 1 1 1 1 1 0 0 2 1 1 0 0 0 1 0 3 3 0 1 0 0 0 1 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 2 2 2 2 2 , 0 , 0 1 0 0 0 1 0 0 0 0 0 0 2 0 0 3 3 0 2 0 0 0 0 0 2 , 1 ) acting on the columns of the generator matrix as follows (in order): (5, 6), (1, 2)(4, 8) orbits: { 1, 2 }, { 3 }, { 4, 8 }, { 5, 6 }, { 7 } code no 18: ================ 1 1 1 1 1 1 0 0 2 1 1 0 0 0 1 0 3 3 1 1 0 0 0 1 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 0 3 3 3 3 3 , 0 , 3 0 0 0 0 1 2 2 0 0 0 0 2 0 0 1 1 3 3 0 3 3 3 3 3 , 1 ) acting on the columns of the generator matrix as follows (in order): (5, 6), (2, 7)(4, 8)(5, 6) orbits: { 1 }, { 2, 7 }, { 3 }, { 4, 8 }, { 5, 6 } code no 19: ================ 1 1 1 1 1 1 0 0 2 1 1 0 0 0 1 0 1 2 2 1 0 0 0 1 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 0 3 3 3 3 3 , 0 , 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 , 0 , 2 3 3 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 2 , 1 ) acting on the columns of the generator matrix as follows (in order): (5, 6), (2, 3)(5, 6), (1, 7) orbits: { 1, 7 }, { 2, 3 }, { 4 }, { 5, 6 }, { 8 } code no 20: ================ 1 1 1 1 1 1 0 0 2 1 1 0 0 0 1 0 2 2 2 1 0 0 0 1 the automorphism group has order 16 and is strongly generated by the following 4 elements: ( 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 0 3 3 3 3 3 , 0 , 2 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 2 , 0 , 0 0 0 1 0 1 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 , 0 , 2 2 2 3 0 3 3 3 3 3 0 0 0 0 3 1 2 2 0 0 0 3 0 0 0 , 1 ) acting on the columns of the generator matrix as follows (in order): (5, 6), (2, 3), (1, 4)(2, 5, 3, 6)(7, 8), (1, 8)(2, 5, 3, 6)(4, 7) orbits: { 1, 4, 8, 7 }, { 2, 3, 6, 5 } code no 21: ================ 1 1 1 1 1 1 0 0 2 1 1 0 0 0 1 0 0 3 3 1 0 0 0 1 the automorphism group has order 32 and is strongly generated by the following 5 elements: ( 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 2 2 2 2 2 , 0 , 3 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 1 1 3 0 0 0 0 0 3 , 1 , 3 0 0 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 3 , 0 , 1 2 2 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 1 0 0 0 0 0 1 , 1 , 0 1 1 2 0 0 0 2 0 0 0 2 0 0 0 2 1 1 0 0 0 0 0 0 2 , 0 ) acting on the columns of the generator matrix as follows (in order): (5, 6), (4, 8), (2, 3), (1, 7)(2, 3), (1, 8)(2, 3)(4, 7) orbits: { 1, 7, 8, 4 }, { 2, 3 }, { 5, 6 } code no 22: ================ 1 1 1 1 1 1 0 0 2 1 1 0 0 0 1 0 2 1 0 2 1 0 0 1 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 0 0 2 0 0 2 3 3 0 0 2 0 0 0 0 1 2 0 1 2 0 0 0 0 3 , 1 ) acting on the columns of the generator matrix as follows (in order): (1, 3)(2, 7)(4, 8) orbits: { 1, 3 }, { 2, 7 }, { 4, 8 }, { 5 }, { 6 } code no 23: ================ 1 1 1 1 1 1 0 0 2 1 1 0 0 0 1 0 2 3 0 2 1 0 0 1 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 2 0 0 0 0 3 2 2 0 0 0 0 2 0 0 0 0 0 0 3 0 0 0 1 0 , 0 , 2 3 3 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 2 0 2 2 2 2 2 , 1 , 0 2 0 0 0 0 0 3 0 0 2 3 3 0 0 0 0 0 0 3 2 1 0 2 3 , 1 ) acting on the columns of the generator matrix as follows (in order): (2, 7)(4, 5)(6, 8), (1, 7)(2, 3)(5, 6), (1, 7, 3, 2)(4, 6, 8, 5) orbits: { 1, 7, 2, 3 }, { 4, 5, 6, 8 } code no 24: ================ 1 1 1 1 1 1 0 0 2 1 1 0 0 0 1 0 3 3 0 2 1 0 0 1 the automorphism group has order 6 and is strongly generated by the following 3 elements: ( 1 0 0 0 0 2 3 3 0 0 0 0 3 0 0 0 0 0 1 0 0 0 0 0 2 , 1 , 1 2 2 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 1 0 1 1 1 1 1 , 1 , 0 2 0 0 0 2 0 0 0 0 0 0 3 0 0 0 0 0 1 0 1 1 0 2 3 , 1 ) acting on the columns of the generator matrix as follows (in order): (2, 7)(6, 8), (1, 7)(5, 6), (1, 2)(5, 8) orbits: { 1, 7, 2 }, { 3 }, { 4 }, { 5, 6, 8 } code no 25: ================ 1 1 1 1 1 1 0 0 2 1 1 0 0 0 1 0 3 3 3 2 1 0 0 1 the automorphism group has order 48 and is strongly generated by the following 5 elements: ( 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 3 0 1 1 1 1 1 , 0 , 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 2 2 2 2 2 0 0 0 2 0 , 0 , 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 2 2 2 1 3 0 0 0 0 3 , 0 , 2 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 2 , 0 , 3 1 1 0 0 0 2 0 0 0 0 0 2 0 0 3 3 3 3 3 0 0 0 0 3 , 1 ) acting on the columns of the generator matrix as follows (in order): (5, 8, 6), (4, 5, 6), (4, 6, 8), (2, 3), (1, 7)(4, 6) orbits: { 1, 7 }, { 2, 3 }, { 4, 6, 8, 5 } code no 26: ================ 1 1 1 1 1 1 0 0 3 2 1 0 0 0 1 0 2 3 1 0 0 0 0 1 the automorphism group has order 720 and is strongly generated by the following 9 elements: ( 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 , 1 , 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 0 3 3 3 3 3 , 0 , 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 , 0 , 1 0 0 0 0 0 3 0 0 0 3 1 2 0 0 0 0 0 0 2 2 2 2 2 2 , 1 , 2 0 0 0 0 0 1 0 0 0 1 2 3 0 0 0 0 0 0 3 0 0 0 3 0 , 0 , 2 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 2 2 2 2 2 2 , 1 , 2 0 0 0 0 2 3 1 0 0 2 1 3 0 0 0 0 0 2 0 0 0 0 0 2 , 0 , 2 1 3 0 0 3 0 0 0 0 0 0 2 0 0 0 0 0 0 1 1 1 1 1 1 , 0 , 2 1 3 0 0 2 0 0 0 0 2 3 1 0 0 2 2 2 2 2 0 0 0 0 2 , 1 ) acting on the columns of the generator matrix as follows (in order): (7, 8), (5, 6), (4, 6, 5), (3, 7)(4, 6, 5), (3, 7, 8)(4, 5), (2, 3)(4, 6, 5), (2, 8)(3, 7), (1, 2, 7)(4, 6, 5), (1, 2, 8)(3, 7)(4, 6) orbits: { 1, 7, 8, 3, 2 }, { 4, 5, 6 } code no 27: ================ 1 1 1 1 1 1 0 0 3 2 1 0 0 0 1 0 3 2 0 1 0 0 0 1 the automorphism group has order 96 and is strongly generated by the following 6 elements: ( 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 2 2 2 2 2 , 0 , 3 0 0 0 0 0 2 0 0 0 0 0 1 0 0 2 3 0 1 0 0 0 0 0 1 , 1 , 2 0 0 0 0 0 1 0 0 0 1 2 3 0 0 0 0 0 3 0 0 0 0 0 3 , 1 , 3 0 0 0 0 0 2 0 0 0 0 0 0 1 0 2 3 1 0 0 1 1 1 1 1 , 1 , 3 1 2 0 0 0 0 3 0 0 2 0 0 0 0 0 0 0 1 0 1 1 1 1 1 , 1 , 0 0 0 1 0 1 3 0 2 0 0 1 0 0 0 2 1 3 0 0 0 0 0 0 3 , 0 ) acting on the columns of the generator matrix as follows (in order): (5, 6), (4, 8), (3, 7), (3, 8, 7, 4)(5, 6), (1, 3, 2, 7)(5, 6), (1, 7, 4)(2, 3, 8) orbits: { 1, 7, 4, 3, 8, 2 }, { 5, 6 } code no 28: ================ 1 1 1 1 1 1 0 0 3 2 1 0 0 0 1 0 2 3 1 1 0 0 0 1 the automorphism group has order 16 and is strongly generated by the following 3 elements: ( 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 0 3 3 3 3 3 , 0 , 2 0 0 0 0 0 1 0 0 0 1 2 3 0 0 0 0 0 3 0 0 0 0 0 3 , 1 , 0 0 2 0 0 1 2 3 0 0 0 3 0 0 0 0 0 0 1 0 1 1 1 1 1 , 1 ) acting on the columns of the generator matrix as follows (in order): (5, 6), (3, 7), (1, 7, 2, 3)(5, 6) orbits: { 1, 3, 7, 2 }, { 4 }, { 5, 6 }, { 8 } code no 29: ================ 1 1 1 1 1 1 0 0 3 2 1 0 0 0 1 0 2 1 0 2 1 0 0 1 the automorphism group has order 24 and is strongly generated by the following 3 elements: ( 2 0 0 0 0 0 1 0 0 0 1 2 3 0 0 0 0 0 0 3 0 0 0 3 0 , 1 , 2 0 0 0 0 3 2 1 0 0 0 3 0 0 0 0 0 0 0 1 1 1 1 1 1 , 0 , 2 1 3 0 0 3 0 0 0 0 0 0 2 0 0 0 0 0 0 1 1 1 1 1 1 , 0 ) acting on the columns of the generator matrix as follows (in order): (3, 7)(4, 5), (2, 3, 7)(4, 6, 5), (1, 2, 7)(4, 6, 5) orbits: { 1, 7, 3, 2 }, { 4, 5, 6 }, { 8 } code no 30: ================ 1 1 1 1 1 1 0 0 3 2 1 0 0 0 1 0 3 2 0 2 1 0 0 1 the automorphism group has order 16 and is strongly generated by the following 3 elements: ( 1 0 0 0 0 0 3 0 0 0 0 0 2 0 0 0 0 0 3 0 3 1 0 1 2 , 1 , 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 , 1 , 0 2 0 0 0 1 0 0 0 0 2 1 3 0 0 0 0 0 3 0 0 0 0 0 3 , 0 ) acting on the columns of the generator matrix as follows (in order): (5, 8), (2, 3)(4, 6), (1, 2)(3, 7) orbits: { 1, 2, 3, 7 }, { 4, 6 }, { 5, 8 } code no 31: ================ 1 1 1 1 1 1 0 0 3 2 1 0 0 0 1 0 3 3 3 2 1 0 0 1 the automorphism group has order 576 and is strongly generated by the following 6 elements: ( 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 3 0 1 1 1 3 2 , 0 , 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 2 2 2 2 2 0 0 0 2 0 , 0 , 2 0 0 0 0 0 1 0 0 0 1 2 3 0 0 0 0 0 0 3 0 0 0 3 0 , 1 , 3 0 0 0 0 0 0 3 0 0 0 3 0 0 0 3 3 3 3 3 0 0 0 0 3 , 1 , 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 , 0 , 3 3 3 2 1 1 1 1 1 1 0 0 0 3 0 0 0 2 0 0 0 2 0 0 0 , 0 ) acting on the columns of the generator matrix as follows (in order): (5, 6, 8), (4, 5, 6), (3, 7)(4, 5), (2, 3)(4, 6), (1, 2, 3)(4, 6, 5), (1, 6, 2, 5, 7, 8)(3, 4) orbits: { 1, 3, 8, 7, 2, 4, 6, 5 } code no 32: ================ 1 1 1 1 1 1 0 0 2 2 1 1 0 0 1 0 3 3 1 1 0 0 0 1 the automorphism group has order 96 and is strongly generated by the following 5 elements: ( 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 , 1 , 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 1 , 0 , 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 , 0 , 3 0 0 0 0 0 3 0 0 0 3 3 3 3 3 0 0 0 0 3 0 0 0 3 0 , 1 , 2 2 2 2 2 0 0 0 0 2 0 0 2 0 0 0 0 0 2 0 2 0 0 0 0 , 1 ) acting on the columns of the generator matrix as follows (in order): (7, 8), (5, 6), (3, 4), (3, 6)(4, 5), (1, 5, 2, 6) orbits: { 1, 6, 5, 3, 2, 4 }, { 7, 8 } code no 33: ================ 1 1 1 1 1 1 0 0 2 2 1 1 0 0 1 0 2 1 2 1 0 0 0 1 the automorphism group has order 16 and is strongly generated by the following 4 elements: ( 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 1 , 0 , 1 0 0 0 0 3 2 3 2 0 3 3 2 2 0 0 0 0 1 0 1 1 1 1 1 , 0 , 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 , 0 , 0 0 0 3 0 0 0 3 0 0 0 3 0 0 0 3 0 0 0 0 0 0 0 0 3 , 1 ) acting on the columns of the generator matrix as follows (in order): (5, 6), (2, 8)(3, 7)(5, 6), (2, 3)(7, 8), (1, 4)(2, 3) orbits: { 1, 4 }, { 2, 8, 3, 7 }, { 5, 6 } code no 34: ================ 1 1 1 1 1 1 0 0 3 2 1 1 0 0 1 0 2 3 1 1 0 0 0 1 the automorphism group has order 192 and is strongly generated by the following 8 elements: ( 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 , 1 , 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 2 2 2 2 2 , 0 , 3 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 3 , 0 , 3 0 0 0 0 0 3 0 0 0 0 0 0 0 3 3 3 3 3 3 0 0 0 3 0 , 1 , 2 0 0 0 0 1 3 2 2 0 0 0 0 0 3 3 3 3 3 3 0 0 0 1 0 , 0 , 3 0 0 0 0 2 1 3 3 0 0 0 0 0 1 1 1 1 1 1 0 0 2 0 0 , 1 , 1 2 3 3 0 0 3 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 1 , 1 , 1 2 3 3 0 2 1 3 3 0 0 0 0 0 3 3 3 3 3 3 0 0 0 3 0 , 0 ) acting on the columns of the generator matrix as follows (in order): (7, 8), (5, 6), (3, 4), (3, 6, 4, 5), (2, 7)(3, 6, 4, 5), (2, 7, 8)(3, 5)(4, 6), (1, 7), (1, 7, 2, 8)(3, 6, 4, 5) orbits: { 1, 7, 8, 2 }, { 3, 4, 5, 6 } code no 35: ================ 1 1 1 0 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 0 1 the automorphism group has order 768 and is strongly generated by the following 8 elements: ( 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 , 1 , 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 0 3 3 0 0 3 , 1 , 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 3 3 0 3 0 0 0 0 0 3 , 1 , 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 , 1 , 3 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 3 , 1 , 0 3 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 , 1 , 2 2 0 2 0 0 0 0 2 0 2 2 2 0 0 2 0 0 0 0 0 0 0 0 2 , 1 , 0 0 0 0 2 2 2 0 0 2 0 0 0 2 0 2 2 2 0 0 0 2 0 0 0 , 1 ) acting on the columns of the generator matrix as follows (in order): id, (5, 8), (4, 7), (4, 5, 7, 8), (3, 4)(6, 7), (1, 2), (1, 4, 2, 7)(3, 6), (1, 8, 2, 5)(3, 7, 6, 4) orbits: { 1, 2, 7, 5, 4, 8, 6, 3 } code no 36: ================ 1 1 1 0 0 1 0 0 1 1 0 1 0 0 1 0 2 1 0 0 1 0 0 1 the automorphism group has order 32 and is strongly generated by the following 5 elements: ( 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 0 1 3 0 0 3 , 0 , 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 1 , 0 , 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 1 , 0 , 3 0 0 0 0 0 3 0 0 0 0 0 0 3 0 3 3 3 0 0 0 0 0 0 3 , 0 , 0 2 0 0 0 2 0 0 0 0 2 2 2 0 0 0 0 0 2 0 0 0 0 0 3 , 1 ) acting on the columns of the generator matrix as follows (in order): (5, 8), (4, 7), (3, 6), (3, 7, 6, 4), (1, 2)(3, 6) orbits: { 1, 2 }, { 3, 6, 4, 7 }, { 5, 8 } code no 37: ================ 1 1 1 0 0 1 0 0 1 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 the automorphism group has order 96 and is strongly generated by the following 6 elements: ( 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 , 1 , 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 2 0 2 2 2 , 0 , 3 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 3 , 1 , 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 1 , 0 , 0 0 2 0 0 2 2 2 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 2 , 0 , 3 3 3 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 3 , 1 ) acting on the columns of the generator matrix as follows (in order): id, (5, 8), (3, 4)(6, 7), (3, 6)(4, 7), (1, 4, 3)(2, 7, 6), (1, 6)(2, 3) orbits: { 1, 3, 6, 4, 2, 7 }, { 5, 8 } code no 38: ================ 1 1 1 0 0 1 0 0 3 2 1 1 0 0 1 0 3 2 1 0 1 0 0 1 the automorphism group has order 192 and is strongly generated by the following 6 elements: ( 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 3 2 1 0 1 , 0 , 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 2 1 3 3 0 0 0 0 0 3 , 0 , 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 2 1 3 0 3 2 1 3 3 0 , 0 , 3 0 0 0 0 0 3 0 0 0 3 3 3 0 0 0 0 0 3 0 0 0 0 0 3 , 1 , 2 0 0 0 0 2 2 2 0 0 0 0 2 0 0 0 0 0 1 0 0 0 0 0 1 , 1 , 0 0 3 0 0 3 0 0 0 0 0 3 0 0 0 0 0 0 2 0 0 0 0 0 2 , 0 ) acting on the columns of the generator matrix as follows (in order): (5, 8), (4, 7), (4, 8)(5, 7), (3, 6), (2, 6), (1, 2, 3) orbits: { 1, 3, 6, 2 }, { 4, 7, 8, 5 }