the 3 isometry classes of irreducible [9,6,3]_3 codes are: code no 1: ================ 1 1 1 2 0 0 0 0 0 1 1 0 0 2 0 0 0 0 2 1 0 0 0 2 0 0 0 1 0 1 0 0 0 2 0 0 2 0 1 0 0 0 0 2 0 0 1 1 0 0 0 0 0 2 the automorphism group has order 12 and is strongly generated by the following 3 elements: ( 2 0 0 0 1 0 1 0 1 , 2 0 0 0 0 2 0 2 0 , 2 0 0 1 0 2 2 2 0 ) acting on the columns of the generator matrix as follows (in order): (3, 7)(4, 9)(5, 6), (2, 3)(5, 7)(6, 8), (2, 8)(3, 5)(6, 7) orbits: { 1 }, { 2, 3, 8, 7, 5, 6 }, { 4, 9 } code no 2: ================ 1 1 1 2 0 0 0 0 0 1 1 0 0 2 0 0 0 0 2 1 0 0 0 2 0 0 0 1 0 1 0 0 0 2 0 0 2 0 1 0 0 0 0 2 0 0 2 1 0 0 0 0 0 2 the automorphism group has order 24 and is strongly generated by the following 4 elements: ( 1 0 0 0 1 0 2 0 2 , 2 0 0 1 1 0 1 0 1 , 1 0 0 2 0 2 2 2 0 , 2 1 0 0 1 2 0 1 0 ) acting on the columns of the generator matrix as follows (in order): (3, 7)(4, 9), (2, 5)(3, 7), (2, 7)(3, 5)(6, 8), (1, 8, 6)(2, 3, 9)(4, 5, 7) orbits: { 1, 6, 8 }, { 2, 5, 7, 9, 3, 4 } code no 3: ================ 1 1 1 2 0 0 0 0 0 1 1 0 0 2 0 0 0 0 2 0 1 0 0 2 0 0 0 2 1 1 0 0 0 2 0 0 0 2 1 0 0 0 0 2 0 1 2 1 0 0 0 0 0 2 the automorphism group has order 432 and is strongly generated by the following 5 elements: ( 1 0 0 0 1 0 2 1 1 , 1 0 0 0 1 0 2 2 2 , 1 0 0 2 2 0 2 1 1 , 1 0 0 2 0 1 2 2 2 , 0 1 0 0 0 2 1 1 0 ) acting on the columns of the generator matrix as follows (in order): (3, 9, 7)(4, 6, 8), (3, 4)(6, 7)(8, 9), (2, 5)(3, 7)(4, 6), (2, 7, 6)(3, 5, 4), (1, 6, 7, 4, 8, 5, 3, 2) orbits: { 1, 2, 5, 6, 3, 8, 4, 7, 9 }