the 2 isometry classes of irreducible [8,5,4]_8 codes are: code no 1: ================ 1 1 1 1 0 0 0 0 3 2 1 0 1 0 0 0 5 3 1 0 0 1 0 0 2 4 1 0 0 0 1 0 7 5 1 0 0 0 0 1 the automorphism group has order 42 and is strongly generated by the following 5 elements: ( 1 0 0 5 7 3 1 1 1 , 1 , 7 0 0 6 6 6 1 2 6 , 0 , 7 3 6 5 1 6 0 2 0 , 1 , 0 0 2 4 7 6 1 0 0 , 0 , 7 5 1 7 3 5 5 3 1 , 0 ) acting on the columns of the generator matrix as follows (in order): (2, 7, 6)(3, 8, 4), (2, 4)(3, 7)(6, 8), (1, 4, 6)(2, 3, 7), (1, 3)(2, 6)(4, 7), (1, 8)(2, 7)(3, 6) orbits: { 1, 6, 3, 8, 7, 4, 2 }, { 5 } code no 2: ================ 1 1 1 1 0 0 0 0 3 2 1 0 1 0 0 0 7 3 1 0 0 1 0 0 6 5 1 0 0 0 1 0 2 6 1 0 0 0 0 1 the automorphism group has order 168 and is strongly generated by the following 4 elements: ( 1 0 0 0 3 0 3 6 1 , 2 , 7 0 0 1 4 7 6 5 7 , 1 , 6 0 0 2 6 1 4 6 5 , 0 , 0 0 6 1 2 4 2 2 2 , 2 ) acting on the columns of the generator matrix as follows (in order): (3, 5, 7)(4, 8, 6), (2, 4, 7)(3, 5, 6), (2, 7, 3, 4, 5, 6, 8), (1, 4, 3)(2, 5, 7) orbits: { 1, 3, 7, 6, 4, 5, 2, 8 }