the 3 isometry classes of irreducible [8,2,5]_3 codes are: code no 1: ================ 1 1 1 1 1 1 2 0 2 1 1 1 0 0 0 2 the automorphism group has order 144 and is strongly generated by the following 5 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 1 1 1 1 1 1 , 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 0 2 0 0 0 0 2 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 0 0 0 0 0 2 , 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 2 2 2 2 2 2 0 0 1 0 0 0 0 1 0 0 0 0 , 1 2 2 2 0 0 0 0 0 0 0 1 0 0 0 0 1 0 2 2 2 2 2 2 0 2 0 0 0 0 0 0 2 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (6, 7), (5, 6), (3, 4), (2, 6, 3, 5)(4, 7), (1, 8)(2, 5, 3, 6)(4, 7) orbits: { 1, 8 }, { 2, 5, 6, 3, 7, 4 } code no 2: ================ 1 1 1 1 1 1 2 0 2 2 1 1 0 0 0 2 the automorphism group has order 48 and is strongly generated by the following 5 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 1 1 1 1 1 1 , 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 0 2 0 0 0 0 2 0 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 2 2 2 2 2 2 0 0 0 0 0 1 , 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 2 2 2 2 2 2 0 0 0 0 1 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 0 0 0 0 0 2 ) acting on the columns of the generator matrix as follows (in order): (6, 7), (5, 6), (3, 4)(5, 7), (1, 4)(2, 3)(5, 6, 7), (1, 2) orbits: { 1, 4, 2, 3 }, { 5, 6, 7 }, { 8 } code no 3: ================ 1 1 1 1 0 0 2 0 1 1 0 0 1 1 0 2 the automorphism group has order 144 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 1 1 0 0 1 1 , 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 0 2 0 0 0 0 2 0 , 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 1 1 1 1 0 0 0 0 0 0 2 0 0 0 0 0 0 2 , 1 0 0 0 0 0 0 1 0 0 0 0 2 2 2 2 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 2 2 0 0 2 2 0 0 0 0 1 0 0 0 1 0 0 0 2 2 2 2 0 0 , 0 2 0 0 0 0 2 0 0 0 0 0 1 1 1 1 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 ) acting on the columns of the generator matrix as follows (in order): (6, 8), (5, 6), (4, 7), (3, 7), (3, 5, 4, 8)(6, 7), (1, 2)(3, 4, 7) orbits: { 1, 2 }, { 3, 7, 8, 4, 6, 5 }