the 1 isometry classes of irreducible [9,4,6]_8 codes are: code no 1: ================ 1 1 1 1 1 1 0 0 0 5 4 3 2 1 0 1 0 0 4 3 6 5 1 0 0 1 0 2 5 4 7 1 0 0 0 1 the automorphism group has order 1512 and is strongly generated by the following 7 elements: ( 6 0 0 0 0 0 4 0 0 0 0 0 5 0 0 4 4 4 4 4 1 2 7 3 5 , 1 , 2 0 0 0 0 0 6 0 0 0 0 0 0 0 3 3 7 6 1 2 1 1 1 1 1 , 2 , 5 0 0 0 0 0 4 0 0 0 2 6 3 7 4 0 0 0 2 0 0 0 5 0 0 , 2 , 4 0 0 0 0 0 0 2 0 0 5 5 5 5 5 0 0 0 0 6 1 5 7 2 3 , 0 , 7 5 3 6 1 4 0 0 0 0 0 0 0 0 7 3 5 4 2 6 0 0 7 0 0 , 2 , 0 0 0 0 7 0 5 0 0 0 0 0 0 3 0 2 2 2 2 2 2 7 4 1 5 , 1 , 7 2 6 5 4 7 4 2 1 3 0 7 0 0 0 0 0 0 1 0 2 1 4 5 7 , 2 ) acting on the columns of the generator matrix as follows (in order): (4, 7, 6)(5, 8, 9), (3, 6, 5)(4, 7, 8), (3, 5, 7)(6, 8, 9), (2, 7, 8, 5, 4, 6, 3), (1, 2, 7, 4, 6, 8)(3, 5), (1, 7, 5)(3, 6, 4), (1, 6, 7, 2, 3, 9)(5, 8) orbits: { 1, 8, 5, 9, 7, 6, 3, 4, 2 }