the 1 isometry classes of irreducible [13,9,3]_2 codes are: code no 1: ================ 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 the automorphism group has order 192 and is strongly generated by the following 6 elements: ( 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 , 1 0 0 0 0 1 0 0 1 1 1 0 1 1 0 1 , 1 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 , 1 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 , 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 , 0 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 ) acting on the columns of the generator matrix as follows (in order): (4, 12)(5, 13)(10, 11), (3, 9)(4, 12)(7, 8)(10, 11), (3, 12)(4, 9)(7, 11)(8, 10), (3, 8)(4, 11)(7, 9)(10, 12), (1, 2)(7, 8)(10, 11), (1, 8, 5, 4)(2, 7, 13, 12)(3, 11)(9, 10) orbits: { 1, 2, 4, 12, 9, 11, 5, 3, 10, 13, 7, 8 }, { 6 }