the 3 isometry classes of irreducible [8,4,4]_3 codes are: code no 1: ================ 1 1 1 1 2 0 0 0 2 1 1 0 0 2 0 0 2 1 0 1 0 0 2 0 2 0 1 1 0 0 0 2 the automorphism group has order 192 and is strongly generated by the following 5 elements: ( 1 0 0 0 0 1 0 0 0 0 1 0 2 2 2 2 , 2 0 0 0 0 2 0 0 0 0 0 2 0 0 2 0 , 2 0 0 0 0 0 2 0 0 2 0 0 1 1 1 1 , 1 2 0 2 0 0 1 0 2 2 2 2 0 0 0 2 , 0 2 0 0 1 2 0 2 2 0 0 0 1 2 2 0 ) acting on the columns of the generator matrix as follows (in order): (4, 5)(7, 8), (3, 4)(6, 7), (2, 3)(4, 5), (1, 6, 7)(2, 5, 3), (1, 3, 8, 5, 7, 2)(4, 6) orbits: { 1, 7, 2, 8, 6, 5, 3, 4 } code no 2: ================ 1 1 1 1 2 0 0 0 2 1 1 0 0 2 0 0 2 1 0 1 0 0 2 0 0 2 1 1 0 0 0 2 the automorphism group has order 24 and is strongly generated by the following 4 elements: ( 2 0 0 0 0 2 0 0 0 0 2 0 0 2 1 1 , 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 , 2 1 0 1 0 0 0 1 0 1 0 0 0 0 2 0 , 1 1 1 1 0 2 1 1 0 0 0 1 0 2 0 0 ) acting on the columns of the generator matrix as follows (in order): (4, 8)(5, 7), (3, 4)(6, 7), (1, 6, 7)(2, 3, 4), (1, 7, 6, 5)(2, 4, 3, 8) orbits: { 1, 7, 5, 6 }, { 2, 4, 8, 3 } code no 3: ================ 1 1 1 1 2 0 0 0 2 1 1 0 0 2 0 0 1 2 0 1 0 0 2 0 2 2 1 1 0 0 0 2 the automorphism group has order 32 and is strongly generated by the following 5 elements: ( 2 0 0 0 0 2 0 0 2 1 0 2 1 2 2 0 , 1 0 0 0 0 1 0 0 0 0 0 2 0 0 2 0 , 0 1 0 0 1 0 0 0 2 1 1 0 1 2 0 1 , 2 2 1 1 2 2 2 2 2 1 0 2 0 0 0 1 , 0 0 2 0 1 2 0 1 1 0 0 0 1 1 1 1 ) acting on the columns of the generator matrix as follows (in order): (3, 7)(4, 6), (3, 4)(5, 8)(6, 7), (1, 2)(3, 6)(4, 7), (1, 8)(2, 5)(3, 7), (1, 3)(2, 7)(4, 5)(6, 8) orbits: { 1, 2, 8, 3, 5, 7, 6, 4 }