the 8 isometry classes of irreducible [9,3,4]_2 codes are: code no 1: ================ 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 1 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 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 , 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (6, 7), (5, 6, 7), (3, 9)(4, 8)(5, 6, 7), (3, 4)(5, 6)(8, 9), (1, 2)(5, 7) orbits: { 1, 2 }, { 3, 9, 4, 8 }, { 5, 7, 6 } code no 2: ================ 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 1 0 1 0 0 1 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 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 , 1 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 0 1 0 0 1 1 1 1 1 1 , 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 1 1 1 , 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 ) acting on the columns of the generator matrix as follows (in order): (6, 7), (4, 5)(6, 7), (2, 3)(4, 5)(6, 7), (2, 5)(3, 4)(6, 7)(8, 9) orbits: { 1 }, { 2, 3, 5, 4 }, { 6, 7 }, { 8, 9 } code no 3: ================ 1 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0 1 1 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 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 1 , 1 0 0 0 0 0 0 1 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 0 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 ) acting on the columns of the generator matrix as follows (in order): (6, 9), (5, 6), (5, 6, 9), (4, 8), (3, 8, 7, 4)(5, 6) orbits: { 1 }, { 2 }, { 3, 4, 8, 7 }, { 5, 6, 9 } code no 4: ================ 1 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 0 1 1 0 0 1 1 0 0 1 the automorphism group has order 288 and is strongly generated by the following 7 elements: ( 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 , 1 0 0 0 0 0 0 1 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 0 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 , 1 1 1 0 0 0 0 0 1 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 1 0 , 1 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (6, 9), (5, 6), (5, 6, 9), (4, 8), (3, 8)(4, 7), (1, 7)(2, 3)(5, 6), (1, 4, 2, 8)(3, 7) orbits: { 1, 7, 8, 4, 3, 2 }, { 5, 6, 9 } code no 5: ================ 1 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 1 1 0 0 1 the automorphism group has order 144 and is strongly generated by the following 6 elements: ( 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 1 1 , 1 0 0 0 0 0 0 1 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 0 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 0 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 , 1 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (6, 9), (5, 6), (5, 6, 9), (3, 7)(4, 8)(5, 6), (3, 8)(4, 7), (1, 4, 2, 8)(3, 7) orbits: { 1, 8, 4, 3, 2, 7 }, { 5, 6, 9 } code no 6: ================ 1 1 1 0 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 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 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 , 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (6, 9), (5, 8), (3, 7), (2, 4)(3, 8)(5, 7), (1, 4)(3, 9)(6, 7) orbits: { 1, 4, 2 }, { 3, 7, 8, 9, 5, 6 } code no 7: ================ 1 1 1 0 0 0 1 0 0 1 1 0 1 1 0 0 1 0 1 1 0 1 0 1 0 0 1 the automorphism group has order 128 and is strongly generated by the following 6 elements: ( 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 1 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 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 0 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 , 1 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 , 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 1 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (6, 9), (5, 8), (5, 6)(8, 9), (3, 7), (1, 7)(2, 3), (1, 5, 3, 9)(2, 8, 7, 6) orbits: { 1, 7, 9, 3, 8, 6, 2, 5 }, { 4 } code no 8: ================ 1 1 1 0 0 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 1 0 1 0 0 1 the automorphism group has order 32 and is strongly generated by the following 5 elements: ( 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 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 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 0 1 1 0 , 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 0 0 0 0 0 1 , 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (6, 9), (5, 8), (2, 3)(5, 9)(6, 8), (1, 2)(3, 7)(5, 8), (1, 3)(2, 7) orbits: { 1, 2, 3, 7 }, { 4 }, { 5, 8, 9, 6 }