the 2 isometry classes of irreducible [5,2,3]_8 codes are: code no 1: ================ 1 1 1 1 0 1 1 0 0 1 the automorphism group has order 24 and is strongly generated by the following 3 elements: ( 3 0 0 0 3 0 0 0 3 , 2 , 2 0 0 0 2 0 2 2 2 , 2 , 4 4 4 0 0 4 4 0 0 , 0 ) acting on the columns of the generator matrix as follows (in order): id, (3, 4), (1, 3, 2, 4) orbits: { 1, 4, 3, 2 }, { 5 } code no 2: ================ 1 1 1 1 0 2 1 0 0 1 the automorphism group has order 6 and is strongly generated by the following 2 elements: ( 1 0 0 0 1 0 1 1 1 , 0 , 1 3 0 2 0 0 3 3 3 , 2 ) acting on the columns of the generator matrix as follows (in order): (3, 4), (1, 2, 5)(3, 4) orbits: { 1, 5, 2 }, { 3, 4 }