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