the 2 isometry classes of irreducible [9,6,4]_8 codes are: code no 1: ================ 1 1 1 1 0 0 0 0 0 3 2 1 0 1 0 0 0 0 5 3 1 0 0 1 0 0 0 2 4 1 0 0 0 1 0 0 7 5 1 0 0 0 0 1 0 4 6 1 0 0 0 0 0 1 the automorphism group has order 168 and is strongly generated by the following 4 elements: ( 1 0 0 0 1 0 2 4 7 , 2 , 1 0 0 5 7 3 1 1 1 , 1 , 3 0 0 0 0 3 4 5 2 , 0 , 0 0 3 4 5 2 3 3 3 , 0 ) acting on the columns of the generator matrix as follows (in order): (3, 7, 9)(4, 6, 8), (2, 7, 6)(3, 8, 4), (2, 8, 4, 9, 6, 7, 3), (1, 7, 2, 8, 6, 4, 3) orbits: { 1, 3, 9, 4, 7, 8, 6, 2 }, { 5 } code no 2: ================ 1 1 1 1 0 0 0 0 0 3 2 1 0 1 0 0 0 0 7 3 1 0 0 1 0 0 0 6 5 1 0 0 0 1 0 0 2 6 1 0 0 0 0 1 0 4 7 1 0 0 0 0 0 1 the automorphism group has order 1512 and is strongly generated by the following 5 elements: ( 5 0 0 0 4 0 0 0 1 , 2 , 1 0 0 0 3 0 3 6 1 , 2 , 7 0 0 1 4 7 6 5 7 , 1 , 0 0 6 1 2 4 2 2 2 , 2 , 3 6 7 0 6 0 4 2 3 , 1 ) acting on the columns of the generator matrix as follows (in order): (4, 6, 5)(7, 9, 8), (3, 5, 7)(4, 8, 6), (2, 4, 7)(3, 5, 6), (1, 4, 3)(2, 5, 7), (1, 8, 3, 6, 4, 9)(5, 7) orbits: { 1, 3, 9, 7, 6, 4, 8, 5, 2 }