the 2 isometry classes of irreducible [8,5,4]_9 codes are: code no 1: ================ 1 1 1 2 0 0 0 0 3 2 1 0 2 0 0 0 2 3 1 0 0 2 0 0 8 4 1 0 0 0 2 0 5 6 1 0 0 0 0 2 the automorphism group has order 16 and is strongly generated by the following 3 elements: ( 2 0 0 5 5 5 8 5 7 , 0 , 3 2 1 0 2 0 3 5 6 , 0 , 6 7 8 8 7 4 7 7 7 , 1 ) acting on the columns of the generator matrix as follows (in order): (2, 4)(3, 5)(7, 8), (1, 5)(3, 6)(4, 7), (1, 8)(2, 6)(3, 4)(5, 7) orbits: { 1, 5, 8, 3, 7, 6, 4, 2 } code no 2: ================ 1 1 1 2 0 0 0 0 3 2 1 0 2 0 0 0 6 3 1 0 0 2 0 0 7 4 1 0 0 0 2 0 4 5 1 0 0 0 0 2 the automorphism group has order 32 and is strongly generated by the following 5 elements: ( 4 0 0 0 6 0 7 4 6 , 1 , 2 0 0 0 7 0 3 7 5 , 1 , 0 3 0 6 0 0 0 0 5 , 1 , 8 4 2 6 6 6 7 8 4 , 1 , 2 4 8 0 0 2 7 7 7 , 0 ) acting on the columns of the generator matrix as follows (in order): (3, 8)(4, 6)(5, 7), (3, 5)(7, 8), (1, 2)(4, 6), (1, 6)(2, 4)(3, 5), (1, 8, 4, 3, 2, 7, 6, 5) orbits: { 1, 2, 6, 5, 4, 3, 7, 8 }