the 1 isometry classes of irreducible [8,1,8]_4 codes are: code no 1: ================ 1 1 1 1 1 1 1 1 the automorphism group has order 80640 and is strongly generated by the following 15 elements: ( 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 , 1 , 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 , 1 , 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 , 0 , 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 , 0 , 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 2 2 2 2 2 2 2 0 0 0 0 2 0 0 0 0 0 0 0 2 0 , 0 , 1 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 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 , 0 , 1 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 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 , 0 , 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 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 2 0 0 0 0 0 0 0 0 2 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 , 1 , 3 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 3 , 0 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 , 1 , 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 , 1 , 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 , 0 , 2 2 2 2 2 2 2 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 , 0 ) acting on the columns of the generator matrix as follows (in order): id, (7, 8), (6, 7), (5, 6), (5, 6, 7, 8), (4, 5, 6), (4, 6, 7), (3, 4, 6), (3, 6, 7, 5, 4, 8), (2, 5)(3, 6, 4), (2, 4, 5, 3, 6), (2, 5, 3, 6, 7), (2, 7, 8)(3, 5), (1, 6, 7, 3)(2, 5), (1, 6, 7, 3, 5, 4, 2, 8) orbits: { 1, 3, 8, 6, 4, 5, 7, 2 }