the 1 isometry classes of irreducible [12,4,6]_2 codes are: code no 1: ================ 1 1 1 1 1 0 0 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 0 1 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 1 0 0 0 1 the automorphism group has order 576 and is strongly generated by the following 5 elements: ( 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 1 1 0 0 0 , 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 1 1 0 , 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 , 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 ) acting on the columns of the generator matrix as follows (in order): (4, 6)(5, 7)(9, 10), (3, 4, 6)(5, 11, 7)(8, 10, 9), (2, 3, 7, 12, 11, 4)(5, 6)(8, 9, 10), (1, 8)(2, 11)(5, 7)(9, 10), (1, 7, 9, 2, 10, 5)(3, 6, 4)(8, 11) orbits: { 1, 8, 5, 9, 10, 11, 7, 6, 2, 12, 3, 4 }