the 2 isometry classes of irreducible [12,8,3]_2 codes are: code no 1: ================ 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 1 the automorphism group has order 48 and is strongly generated by the following 5 elements: ( 1 0 0 0 0 1 0 0 1 1 1 0 1 1 0 1 , 1 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 , 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 , 1 0 0 0 1 1 0 0 0 0 1 0 1 0 0 1 , 1 1 0 0 0 1 0 0 0 0 1 0 0 1 0 1 ) acting on the columns of the generator matrix as follows (in order): (3, 9)(4, 12)(7, 8)(10, 11), (3, 12)(4, 9)(7, 11)(8, 10), (3, 7)(4, 10)(8, 9)(11, 12), (2, 6)(4, 10)(8, 9), (1, 6)(4, 11)(7, 9) orbits: { 1, 6, 2 }, { 3, 9, 12, 7, 4, 8, 11, 10 }, { 5 } code no 2: ================ 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 the automorphism group has order 576 and is strongly generated by the following 8 elements: ( 1 0 0 0 0 1 0 0 0 0 1 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 0 1 0 0 1 1 1 1 0 0 1 0 , 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 , 1 0 0 0 1 1 1 1 1 0 0 1 0 1 0 0 , 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 , 0 0 0 1 1 0 1 0 0 1 0 1 1 0 0 0 , 0 1 1 1 0 0 1 0 1 0 1 1 1 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (4, 5)(9, 12)(10, 11), (3, 4)(7, 9)(8, 10), (3, 4, 5)(7, 9, 12)(8, 10, 11), (2, 7, 9)(3, 4, 6)(8, 11, 10), (2, 4, 7, 5)(3, 12, 6, 9)(10, 11), (1, 10)(2, 9)(3, 5), (1, 4)(2, 7)(3, 10)(5, 8)(6, 11), (1, 4, 12)(2, 11, 3)(5, 9, 8)(6, 7, 10) orbits: { 1, 10, 4, 12, 11, 8, 3, 7, 5, 2, 9, 6 }