the 2 isometry classes of irreducible [8,2,6]_4 codes are: code no 1: ================ 1 1 1 1 1 1 1 0 3 2 2 1 1 0 0 1 the automorphism group has order 96 and is strongly generated by the following 6 elements: ( 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 2 2 2 2 2 2 , 0 , 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 2 , 0 , 3 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 0 0 0 0 3 0 , 1 , 2 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 , 0 , 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 , 0 , 1 2 2 3 3 0 1 1 1 1 1 1 0 0 0 0 0 1 0 3 0 0 0 0 0 0 3 0 0 0 0 0 0 2 0 0 , 1 ) acting on the columns of the generator matrix as follows (in order): (6, 7), (4, 5), (4, 7, 5, 6), (2, 3), (2, 4, 6, 3, 5, 7), (1, 8)(2, 4, 6, 3, 5, 7) orbits: { 1, 8 }, { 2, 3, 7, 6, 4, 5 } code no 2: ================ 1 1 1 1 1 0 1 0 2 2 1 1 0 1 0 1 the automorphism group has order 384 and is strongly generated by the following 7 elements: ( 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 2 2 1 1 0 1 , 0 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 1 , 0 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 1 1 2 2 0 2 0 0 0 0 2 0 , 1 , 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 2 2 2 2 2 0 0 0 2 0 0 0 0 0 0 0 0 2 , 1 , 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 , 0 , 0 0 0 3 0 0 0 0 3 0 0 0 3 3 3 3 3 0 0 0 0 0 3 0 0 3 0 0 0 0 0 0 0 0 0 2 , 0 , 2 2 3 3 0 3 0 0 0 0 0 3 0 2 0 0 0 0 2 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 1 0 , 1 ) acting on the columns of the generator matrix as follows (in order): (6, 8), (5, 7), (5, 6, 7, 8), (3, 5)(4, 7), (1, 2), (1, 7, 3, 2, 5, 4), (1, 4, 5, 6, 2, 3, 7, 8) orbits: { 1, 2, 4, 8, 3, 6, 7, 5 }