the 8 isometry classes of irreducible [9,2,6]_5 codes are: code no 1: ================ 1 1 1 1 1 1 1 4 0 2 2 1 1 1 0 0 0 4 the automorphism group has order 72 and is strongly generated by the following 5 elements: ( 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 3 3 3 3 3 3 3 , 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 0 0 0 0 0 4 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 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 4 4 4 4 4 4 4 , 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 3 3 3 3 3 3 3 , 0 1 0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (7, 8), (6, 7), (4, 5)(7, 8), (3, 4, 5)(7, 8), (1, 2) orbits: { 1, 2 }, { 3, 5, 4 }, { 6, 7, 8 }, { 9 } code no 2: ================ 1 1 1 1 1 1 1 4 0 3 2 1 1 1 0 0 0 4 the automorphism group has order 72 and is strongly generated by the following 6 elements: ( 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 3 3 3 3 3 3 3 , 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 3 , 1 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 1 0 0 0 0 0 0 0 0 1 4 4 4 4 4 4 4 , 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 4 , 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 3 3 3 3 3 3 3 0 0 0 0 0 0 2 , 3 2 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 3 0 2 2 2 2 2 2 2 0 0 0 0 0 0 3 0 0 0 2 0 0 0 0 0 2 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (7, 8), (6, 8), (6, 8, 7), (4, 5)(6, 8), (3, 4)(6, 8), (1, 9)(3, 7, 5, 8, 4, 6) orbits: { 1, 9 }, { 2 }, { 3, 4, 6, 5, 8, 7 } code no 3: ================ 1 1 1 1 1 1 1 4 0 3 3 1 1 1 0 0 0 4 the automorphism group has order 144 and is strongly generated by the following 6 elements: ( 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 3 3 3 3 3 3 3 , 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 3 3 3 3 3 3 3 0 0 0 0 0 2 0 , 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 3 , 3 0 0 0 0 0 0 0 3 0 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 , 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 3 3 3 3 3 3 3 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 , 0 3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 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): (7, 8), (6, 7, 8), (4, 5)(6, 8), (3, 6, 5, 8)(4, 7), (3, 8, 4, 7)(5, 6), (1, 2)(3, 5)(6, 7) orbits: { 1, 2 }, { 3, 8, 7, 5, 6, 4 }, { 9 } code no 4: ================ 1 1 1 1 1 1 1 4 0 3 2 2 1 1 0 0 0 4 the automorphism group has order 24 and is strongly generated by the following 4 elements: ( 1 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 1 0 0 0 0 0 0 0 1 0 4 4 4 4 4 4 4 , 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 1 1 1 1 1 1 1 0 0 0 0 0 4 0 , 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 3 3 3 3 3 3 3 , 3 0 0 0 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 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): (7, 8), (6, 7, 8), (4, 5)(6, 8, 7), (2, 3)(4, 5)(6, 7) orbits: { 1 }, { 2, 3 }, { 4, 5 }, { 6, 8, 7 }, { 9 } code no 5: ================ 1 1 1 1 1 1 1 4 0 4 2 2 1 1 0 0 0 4 the automorphism group has order 48 and is strongly generated by the following 5 elements: ( 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 2 2 2 2 2 2 2 , 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 4 , 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 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 4 4 4 4 4 4 4 , 3 0 0 0 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 3 0 2 2 2 2 2 2 2 , 2 1 1 3 3 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 3 3 3 3 3 3 3 0 0 0 0 0 0 2 ) acting on the columns of the generator matrix as follows (in order): (7, 8), (6, 8), (4, 5)(7, 8), (2, 3)(4, 5)(7, 8), (1, 9)(2, 5, 3, 4)(6, 8) orbits: { 1, 9 }, { 2, 3, 4, 5 }, { 6, 8, 7 } code no 6: ================ 1 1 1 1 1 1 1 4 0 4 3 2 1 1 0 0 0 4 the automorphism group has order 48 and is strongly generated by the following 4 elements: ( 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 3 3 3 3 3 3 3 , 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 3 3 3 3 3 3 3 , 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 4 , 0 2 0 0 0 0 0 0 0 4 0 0 0 0 3 1 4 2 2 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 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): (7, 8), (6, 8, 7), (4, 5)(6, 8), (1, 9, 3, 2)(4, 5)(6, 7) orbits: { 1, 2, 3, 9 }, { 4, 5 }, { 6, 7, 8 } code no 7: ================ 1 1 1 1 1 0 0 4 0 1 1 1 0 0 1 1 0 4 the automorphism group has order 1296 and is strongly generated by the following 11 elements: ( 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 2 2 2 0 0 2 2 , 1 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 , 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 3 3 3 0 0 3 3 0 0 0 0 0 2 0 , 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 3 3 3 3 3 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 , 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 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 4 4 4 4 4 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 , 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 3 3 3 0 0 3 3 0 0 0 0 0 2 0 3 3 3 3 3 0 0 0 0 0 0 2 0 0 , 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 3 3 3 3 3 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 , 0 0 3 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 3 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 , 3 3 3 3 3 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 3 0 , 1 1 1 0 0 1 1 0 0 0 0 0 4 0 0 0 0 0 0 0 4 4 4 4 4 4 0 0 0 0 0 0 1 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (7, 9), (6, 7), (6, 7, 9), (5, 8), (4, 5), (4, 8), (4, 9)(5, 7, 8, 6), (2, 3)(4, 8, 5), (1, 2, 3)(5, 8), (1, 4, 3, 8)(2, 5)(6, 7), (1, 9)(2, 6)(3, 7)(4, 8) orbits: { 1, 3, 8, 9, 2, 4, 7, 5, 6 } code no 8: ================ 1 1 1 1 1 0 0 4 0 2 2 1 1 0 1 1 0 4 the automorphism group has order 96 and is strongly generated by the following 7 elements: ( 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 4 4 2 2 0 2 2 , 1 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 , 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 2 2 1 1 0 1 1 0 0 0 0 0 0 4 , 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 , 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 4 4 4 4 4 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 , 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 , 0 0 0 0 3 0 0 2 2 2 2 2 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 ) acting on the columns of the generator matrix as follows (in order): (7, 9), (6, 7), (6, 9), (5, 8), (3, 4)(5, 8), (1, 2)(3, 4)(6, 7), (1, 8, 2, 5)(3, 4) orbits: { 1, 2, 5, 8 }, { 3, 4 }, { 6, 7, 9 }