the 2 isometry classes of irreducible [6,2,3]_5 codes are: code no 1: ================ 1 1 1 1 4 0 1 1 0 0 0 4 the automorphism group has order 12 and is strongly generated by the following 3 elements: ( 1 0 0 0 0 1 0 0 0 0 1 0 4 4 4 4 , 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 , 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (4, 5), (3, 4), (1, 2) orbits: { 1, 2 }, { 3, 4, 5 }, { 6 } code no 2: ================ 1 1 1 1 4 0 2 1 0 0 0 4 the automorphism group has order 12 and is strongly generated by the following 3 elements: ( 3 0 0 0 0 3 0 0 0 0 3 0 2 2 2 2 , 4 0 0 0 0 4 0 0 1 1 1 1 0 0 0 4 , 2 0 0 0 1 3 0 0 2 2 2 2 0 0 3 0 ) acting on the columns of the generator matrix as follows (in order): (4, 5), (3, 5), (2, 6)(3, 4, 5) orbits: { 1 }, { 2, 6 }, { 3, 5, 4 }