the 1 isometry classes of irreducible [12,3,8]_3 codes are: code no 1: ================ 1 1 1 1 1 1 1 0 0 2 0 0 2 2 1 1 1 0 0 1 1 0 2 0 1 0 2 1 0 2 1 2 1 0 0 2 the automorphism group has order 432 and is strongly generated by the following 6 elements: ( 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 2 2 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 2 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 2 0 0 , 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 2 2 2 2 2 2 2 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 , 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 2 2 1 1 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 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 1 0 2 1 0 2 1 2 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 0 0 2 2 1 1 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2 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 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 2 2 2 0 0 2 2 , 2 2 1 1 1 0 0 1 1 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 1 0 0 0 0 0 0 0 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 0 0 0 1 0 0 1 0 2 1 0 2 1 2 1 ) acting on the columns of the generator matrix as follows (in order): (4, 5)(6, 11)(7, 9)(8, 10), (3, 6)(4, 7)(5, 10)(8, 9), (3, 8)(4, 9)(5, 11)(6, 7), (2, 12)(3, 7, 6, 8, 11, 5)(4, 9, 10), (1, 2)(3, 4)(6, 10)(9, 11), (1, 10, 11)(2, 4, 3)(5, 7, 8)(6, 12, 9) orbits: { 1, 2, 11, 12, 3, 6, 5, 8, 9, 10, 4, 7 }