the 5 isometry classes of irreducible [9,2,6]_4 codes are: code no 1: ================ 1 1 1 1 1 1 1 1 0 2 2 1 1 1 0 0 0 1 the automorphism group has order 144 and is strongly generated by the following 7 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 2 2 2 2 2 2 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 0 0 0 0 2 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 2 , 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 0 0 0 0 0 0 0 1 0 0 0 0 0 1 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 0 3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 , 0 , 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 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 0 0 0 0 3 , 0 , 2 0 0 0 0 0 0 0 2 0 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 , 1 , 0 3 0 0 0 0 0 3 0 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 ) acting on the columns of the generator matrix as follows (in order): (7, 8), (6, 8), (6, 7), (4, 5), (3, 4, 5), (3, 6, 5, 7, 4, 8), (1, 2) orbits: { 1, 2 }, { 3, 5, 8, 4, 6, 7 }, { 9 } code no 2: ================ 1 1 1 1 1 1 1 1 0 3 2 1 1 1 0 0 0 1 the automorphism group has order 432 and is strongly generated by the following 7 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 2 2 2 2 2 2 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 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 , 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 1 1 1 1 1 1 1 0 0 0 0 0 1 0 , 0 , 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 , 1 , 1 0 0 0 0 0 0 3 2 1 1 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 0 0 0 3 0 0 0 0 0 0 0 3 0 0 , 0 , 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 , 1 , 3 1 2 2 2 0 0 2 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 3 0 0 0 0 3 0 0 0 0 , 1 ) acting on the columns of the generator matrix as follows (in order): (7, 8), (6, 7), (4, 5)(6, 7, 8), (3, 6, 5, 7)(4, 8), (2, 9)(3, 8, 5, 7, 4, 6), (1, 2)(3, 5)(6, 8, 7), (1, 2, 9)(3, 7, 5, 6, 4, 8) orbits: { 1, 2, 9 }, { 3, 7, 6, 5, 8, 4 } code no 3: ================ 1 1 1 1 1 1 1 1 0 3 2 2 1 1 0 0 0 1 the automorphism group has order 96 and is strongly generated by the following 6 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 3 3 3 3 3 3 3 , 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 0 1 1 1 1 1 1 1 0 0 0 0 0 0 1 , 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 0 1 1 1 1 1 1 1 1 , 0 , 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 3 3 3 3 3 3 3 , 0 , 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 , 1 , 3 1 1 2 2 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 3 0 3 3 3 3 3 3 3 , 1 ) acting on the columns of the generator matrix as follows (in order): (7, 8), (6, 8), (4, 5)(6, 8, 7), (2, 3)(4, 5)(7, 8), (2, 4)(3, 5)(7, 8), (1, 9)(2, 3)(4, 5)(7, 8) orbits: { 1, 9 }, { 2, 3, 4, 5 }, { 6, 8, 7 } code no 4: ================ 1 1 1 1 1 0 0 1 0 1 1 1 0 0 1 1 0 1 the automorphism group has order 2592 and is strongly generated by the following 10 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 0 0 0 0 0 0 2 , 1 , 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 2 2 2 0 0 2 2 , 1 , 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 0 3 0 0 0 0 0 3 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 0 1 1 1 0 0 1 1 0 0 0 0 0 1 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 3 3 3 3 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 , 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 0 0 0 0 0 0 1 , 1 , 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 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 , 1 , 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 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 , 0 , 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 1 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 , 0 , 1 1 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 1 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): id, (7, 9), (6, 7), (6, 7, 9), (5, 8), (4, 5), (4, 9, 5, 7)(6, 8), (2, 3)(6, 7), (1, 5, 3, 8, 2, 4), (1, 7, 2, 6, 3, 9)(5, 8) orbits: { 1, 4, 9, 5, 7, 2, 3, 8, 6 } code no 5: ================ 1 1 1 1 1 0 0 1 0 2 2 1 1 0 1 1 0 1 the automorphism group has order 288 and is strongly generated by the following 8 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 1 1 3 3 0 3 3 , 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 0 0 0 0 0 0 2 0 0 0 0 0 2 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 0 2 2 1 1 0 1 1 0 0 0 0 0 1 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 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 , 0 , 3 0 0 0 0 0 0 0 3 0 0 0 0 0 3 3 3 3 3 0 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 , 1 , 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 2 2 2 2 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 , 0 , 0 0 0 3 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 0 0 1 0 0 0 0 0 0 0 1 , 1 , 0 3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 3 0 0 3 3 3 3 3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 , 1 ) acting on the columns of the generator matrix as follows (in order): (7, 9), (6, 7), (6, 7, 9), (5, 8), (3, 8)(4, 5), (3, 4)(5, 8)(6, 7), (1, 4)(2, 3), (1, 2)(3, 8, 4, 5) orbits: { 1, 4, 2, 5, 3, 8 }, { 6, 7, 9 }