the 2 isometry classes of irreducible [6,2,3]_3 codes are: code no 1: ================ 1 1 1 1 2 0 1 1 0 0 0 2 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 2 2 2 2 , 1 0 0 0 0 1 0 0 0 0 0 1 2 2 2 2 , 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, 5, 4), (1, 2) orbits: { 1, 2 }, { 3, 4, 5 }, { 6 } code no 2: ================ 1 1 1 1 2 0 2 1 0 0 0 2 the automorphism group has order 36 and is strongly generated by the following 5 elements: ( 2 0 0 0 0 2 0 0 0 0 2 0 1 1 1 1 , 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 , 1 0 0 0 1 2 0 0 0 0 0 2 1 1 1 1 , 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 , 2 1 0 0 0 1 0 0 0 0 0 2 0 0 2 0 ) acting on the columns of the generator matrix as follows (in order): (4, 5), (3, 4), (2, 6)(3, 5, 4), (1, 2), (1, 6)(3, 4) orbits: { 1, 2, 6 }, { 3, 4, 5 }