the 3 isometry classes of irreducible [8,5,3]_3 codes are: code no 1: ================ 1 1 1 2 0 0 0 0 1 1 0 0 2 0 0 0 2 1 0 0 0 2 0 0 1 0 1 0 0 0 2 0 2 0 1 0 0 0 0 2 the automorphism group has order 12 and is strongly generated by the following 3 elements: ( 2 0 0 0 1 0 2 0 1 , 2 0 0 1 1 0 1 0 1 , 1 0 0 1 0 2 0 2 0 ) acting on the columns of the generator matrix as follows (in order): (3, 8)(5, 6), (2, 5)(3, 7), (2, 3, 6, 7, 5, 8) orbits: { 1 }, { 2, 5, 8, 6, 7, 3 }, { 4 } code no 2: ================ 1 1 1 2 0 0 0 0 1 1 0 0 2 0 0 0 2 1 0 0 0 2 0 0 1 0 1 0 0 0 2 0 0 1 1 0 0 0 0 2 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 2 0 0 0 2 0 1 1 1 , 1 0 0 0 2 0 2 0 2 , 0 1 0 1 0 0 2 2 2 ) acting on the columns of the generator matrix as follows (in order): (3, 4)(7, 8), (3, 7)(4, 8)(5, 6), (1, 2)(3, 4) orbits: { 1, 2 }, { 3, 4, 7, 8 }, { 5, 6 } code no 3: ================ 1 1 1 2 0 0 0 0 1 1 0 0 2 0 0 0 2 0 1 0 0 2 0 0 2 1 1 0 0 0 2 0 0 2 1 0 0 0 0 2 the automorphism group has order 48 and is strongly generated by the following 4 elements: ( 1 0 0 2 2 0 2 1 1 , 1 0 0 2 0 1 2 2 2 , 0 2 1 2 2 0 0 2 0 , 0 1 0 0 0 2 1 1 0 ) acting on the columns of the generator matrix as follows (in order): (2, 5)(3, 7)(4, 6), (2, 7, 6)(3, 5, 4), (1, 8)(2, 3, 6, 4, 7, 5), (1, 6, 7, 4, 8, 5, 3, 2) orbits: { 1, 8, 2, 4, 5, 6, 3, 7 }