the 1 isometry classes of irreducible [8,4,4]_2 codes are: code no 1: ================ 1 1 1 0 1 0 0 0 1 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 0 1 1 1 0 0 0 1 the automorphism group has order 1344 and is strongly generated by the following 9 elements: ( 1 0 0 0 0 1 0 0 0 0 1 0 1 0 1 1 , 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 0 0 0 1 0 0 1 0 , 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 , 1 0 0 0 1 0 1 1 0 0 0 1 1 1 0 1 , 1 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 , 1 0 1 1 0 0 1 0 1 1 0 1 1 0 0 0 , 0 1 1 1 0 0 0 1 0 0 1 0 1 0 1 1 ) acting on the columns of the generator matrix as follows (in order): (4, 7)(6, 8), (4, 6)(7, 8), (3, 5)(4, 6), (3, 4)(5, 6), (3, 7)(5, 8), (2, 7)(3, 5, 6, 4), (2, 5, 3)(4, 6, 7), (1, 4, 6, 3, 2, 5, 7), (1, 8)(2, 5, 7, 4) orbits: { 1, 7, 8, 4, 3, 2, 6, 5 }