the 8 isometry classes of irreducible [9,3,5]_3 codes are: code no 1: ================ 1 1 1 1 1 1 2 0 0 2 1 1 1 0 0 0 2 0 1 2 1 0 1 0 0 0 2 the automorphism group has order 24 and is strongly generated by the following 4 elements: ( 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 1 1 1 1 1 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 2 0 0 0 1 2 1 0 1 0 2 1 1 1 0 0 0 0 0 0 0 1 , 1 2 2 2 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 , 1 2 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 2 0 0 1 1 1 1 1 1 ) acting on the columns of the generator matrix as follows (in order): (6, 7), (4, 9)(5, 8), (1, 8)(2, 4), (1, 4, 5, 2, 8, 9)(6, 7) orbits: { 1, 8, 9, 5, 2, 4 }, { 3 }, { 6, 7 } code no 2: ================ 1 1 1 1 1 1 2 0 0 2 1 1 1 0 0 0 2 0 2 2 1 0 1 0 0 0 2 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 1 1 1 1 1 1 , 1 2 2 2 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 2 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, 7), (1, 8)(3, 4) orbits: { 1, 8 }, { 2 }, { 3, 4 }, { 5 }, { 6, 7 }, { 9 } code no 3: ================ 1 1 1 1 1 1 2 0 0 2 1 1 1 0 0 0 2 0 2 2 2 0 1 0 0 0 2 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 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 1 0 0 0 0 0 0 1 0 2 2 2 2 2 2 , 0 0 0 0 1 0 2 2 2 2 2 2 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (6, 7), (2, 3)(6, 7), (1, 5)(2, 6, 3, 7)(8, 9) orbits: { 1, 5 }, { 2, 3, 7, 6 }, { 4 }, { 8, 9 } code no 4: ================ 1 1 1 1 1 1 2 0 0 2 1 1 1 0 0 0 2 0 0 2 1 0 2 1 0 0 2 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 1 0 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 0 0 0 1 0 0 0 0 0 0 1 2 2 2 2 2 2 0 1 0 0 0 0 0 0 1 0 0 0 , 2 1 1 1 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 2 0 0 0 0 2 0 , 0 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2 0 2 1 0 2 1 2 0 0 0 0 0 1 2 2 2 0 0 ) acting on the columns of the generator matrix as follows (in order): (2, 3)(5, 6), (2, 5)(3, 6)(4, 7), (1, 8)(5, 6), (1, 5, 2)(3, 8, 6)(4, 7, 9) orbits: { 1, 8, 2, 3, 5, 6 }, { 4, 7, 9 } code no 5: ================ 1 1 1 1 1 1 2 0 0 2 2 1 1 0 0 0 2 0 2 1 2 0 1 0 0 0 2 the automorphism group has order 12 and is strongly generated by the following 3 elements: ( 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 1 1 1 1 1 1 , 2 0 0 0 0 0 2 1 2 0 1 0 0 0 0 0 1 0 1 1 2 2 0 0 0 0 1 0 0 0 0 0 0 0 0 2 , 2 0 0 0 0 0 0 0 0 0 1 0 2 1 2 0 1 0 0 0 1 0 0 0 1 1 2 2 0 0 1 1 1 1 1 1 ) acting on the columns of the generator matrix as follows (in order): (6, 7), (2, 9)(3, 5)(4, 8), (2, 8, 5)(3, 4, 9)(6, 7) orbits: { 1 }, { 2, 9, 5, 4, 3, 8 }, { 6, 7 } code no 6: ================ 1 1 1 1 1 1 2 0 0 2 2 1 1 0 0 0 2 0 2 0 1 0 2 1 0 0 2 the automorphism group has order 12 and is strongly generated by the following 3 elements: ( 1 0 0 0 0 0 0 0 0 2 0 0 0 0 1 0 0 0 1 1 2 2 0 0 2 0 1 0 2 1 0 0 0 0 2 0 , 1 0 0 0 0 0 2 0 1 0 2 1 0 0 1 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 1 1 2 2 0 0 , 0 0 2 0 0 0 0 0 0 2 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 0 ) acting on the columns of the generator matrix as follows (in order): (2, 8, 4)(5, 6, 9), (2, 9)(4, 5)(6, 8), (1, 3)(2, 4)(5, 6) orbits: { 1, 3 }, { 2, 4, 9, 8, 5, 6 }, { 7 } code no 7: ================ 1 1 1 1 0 0 2 0 0 2 1 1 0 1 0 0 2 0 1 2 1 0 0 1 0 0 2 the automorphism group has order 48 and is strongly generated by the following 5 elements: ( 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 1 2 1 0 0 1 , 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 2 1 1 0 1 0 0 0 0 0 0 2 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 2 2 2 2 0 0 1 2 2 0 2 0 0 0 0 0 0 1 , 2 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 2 2 2 2 0 0 0 0 0 0 0 2 , 0 0 1 0 0 0 0 2 0 0 0 0 1 0 0 0 0 0 2 1 2 0 0 2 2 1 1 0 1 0 2 2 2 2 0 0 ) acting on the columns of the generator matrix as follows (in order): (6, 9), (5, 8), (4, 7)(5, 8), (2, 3)(4, 8, 7, 5), (1, 3)(4, 9)(5, 8)(6, 7) orbits: { 1, 3, 2 }, { 4, 7, 5, 9, 8, 6 } code no 8: ================ 1 1 1 1 0 0 2 0 0 2 1 1 0 1 0 0 2 0 2 1 0 1 0 1 0 0 2 the automorphism group has order 32 and is strongly generated by the following 5 elements: ( 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 2 1 0 1 0 1 , 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 2 1 1 0 1 0 0 0 0 0 0 2 , 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 2 1 0 1 0 1 2 1 1 0 1 0 , 2 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 1 1 1 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 , 1 0 0 0 0 0 2 2 2 2 0 0 0 0 0 1 0 0 0 0 1 0 0 0 2 1 1 0 1 0 0 0 0 0 0 2 ) acting on the columns of the generator matrix as follows (in order): (6, 9), (5, 8), (3, 4)(5, 9)(6, 8), (2, 3)(4, 7), (2, 7)(3, 4)(5, 8) orbits: { 1 }, { 2, 3, 7, 4 }, { 5, 8, 9, 6 }