the 2 isometry classes of irreducible [12,7,4]_2 codes are: code no 1: ================ 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 1 the automorphism group has order 192 and is strongly generated by the following 7 elements: ( 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 1 1 0 0 1 , 1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 1 , 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 1 1 1 , 1 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 1 0 1 0 1 0 1 , 1 1 1 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1 1 1 1 , 1 0 1 1 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 1 1 ) acting on the columns of the generator matrix as follows (in order): (3, 7)(5, 11)(9, 10), (3, 10)(6, 12)(7, 9), (2, 9)(3, 8)(5, 6), (2, 10)(6, 11)(7, 8), (2, 7, 3)(5, 11, 12)(8, 10, 9), (1, 7)(2, 8)(3, 9)(4, 10)(5, 6), (1, 2, 10, 9)(3, 4, 8, 7)(5, 6) orbits: { 1, 7, 9, 3, 8, 2, 10, 4 }, { 5, 11, 6, 12 } code no 2: ================ 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 the automorphism group has order 2304 and is strongly generated by the following 8 elements: ( 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 1 , 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 1 , 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 0 1 , 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 1 0 0 , 1 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 1 1 1 1 , 1 0 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 1 , 1 1 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0 1 1 1 1 1 ) acting on the columns of the generator matrix as follows (in order): (5, 6)(11, 12), (5, 12)(6, 11), (4, 8)(5, 11)(9, 10), (3, 4)(7, 8), (3, 11, 4, 12)(5, 8, 6, 7)(9, 10), (2, 9)(4, 7)(5, 6), (1, 9)(2, 10)(3, 7)(4, 8), (1, 3, 9, 7)(2, 4, 10, 8)(5, 6) orbits: { 1, 9, 7, 10, 2, 3, 8, 6, 4, 12, 5, 11 }