the 1 isometry classes of irreducible [13,3,9]_3 codes are: code no 1: ================ 1 1 1 1 1 1 1 1 0 0 2 0 0 2 2 2 1 1 1 0 0 1 1 0 2 0 2 1 0 2 1 0 2 1 2 1 0 0 2 the automorphism group has order 5616 and is strongly generated by the following 8 elements: ( 2 0 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 2 2 2 0 0 2 2 0 0 0 0 0 0 0 0 0 1 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 1 0 0 , 2 0 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 0 0 0 0 1 0 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 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 , 2 0 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 0 0 0 0 0 0 0 2 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 1 1 1 2 2 2 0 0 2 2 0 0 0 0 0 0 0 0 0 1 , 2 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 2 0 1 2 0 1 2 1 2 0 0 0 0 0 0 0 0 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 1 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 1 0 0 0 0 2 2 2 1 1 1 0 0 1 1 , 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 2 2 2 0 0 2 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 , 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 1 0 2 1 0 2 1 2 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 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 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 , 0 0 0 0 1 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 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 2 2 2 0 0 2 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 , 2 1 0 2 1 0 2 1 2 1 0 0 0 0 0 2 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 2 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 0 0 1 1 1 2 2 2 0 0 2 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 0 0 0 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (5, 6)(7, 12)(8, 10)(9, 11), (4, 5)(7, 10)(8, 9)(11, 12), (4, 8)(5, 11)(6, 7)(9, 12), (3, 13)(4, 5, 7, 11, 12, 10)(6, 9, 8), (2, 3)(4, 11, 12, 5, 7, 10)(6, 8, 9), (2, 12, 13, 4, 3, 7)(5, 10)(6, 8, 9), (1, 4, 3, 5)(2, 6)(7, 10)(8, 9, 11, 12), (1, 11, 6, 2, 5, 3, 10, 12, 7, 8, 9, 4, 13) orbits: { 1, 5, 13, 6, 4, 11, 12, 10, 3, 2, 7, 8, 9 }