the 1 isometry classes of irreducible [24,12,8]_2 codes are: code no 1: ================ 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 244823040 and is strongly generated by the following 16 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 0 1 1 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 1 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 1 1 0 0 1 1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 1 1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 1 0 1 1 0 1 0 1 1 1 0 0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 0 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 1 0 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 1 1 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 , 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 1 0 0 1 1 1 1 1 0 0 0 1 1 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 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 1 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 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 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 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 , 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 , 0 1 1 1 0 0 1 0 0 1 1 1 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 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 , 0 0 1 0 0 1 0 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 1 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 1 0 0 0 1 1 1 0 0 1 0 1 0 1 0 1 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (8, 14)(9, 10)(11, 17)(12, 20)(15, 16)(18, 19)(21, 24)(22, 23), (8, 11)(9, 15)(10, 16)(12, 21)(14, 17)(18, 22)(19, 23)(20, 24), (8, 19)(9, 20)(10, 12)(11, 23)(14, 18)(15, 24)(16, 21)(17, 22), (8, 12)(9, 18)(10, 19)(11, 21)(14, 20)(15, 22)(16, 23)(17, 24), (6, 7, 13)(8, 11, 20)(9, 17, 18)(10, 15, 12)(14, 16, 19)(21, 22, 23), (5, 15)(6, 16)(7, 11)(8, 18)(9, 19)(10, 12)(13, 17)(14, 20), (5, 17)(6, 11)(7, 16)(8, 19)(9, 18)(10, 20)(12, 14)(13, 15), (5, 15, 10)(6, 11, 14)(7, 17, 8)(9, 13, 16)(18, 19, 20)(21, 22, 23), (4, 22, 21)(5, 19, 6)(7, 8, 15)(9, 18, 10)(11, 16, 12)(13, 17, 14), (4, 9, 12)(5, 22, 11)(6, 18, 8)(7, 15, 21)(10, 23, 19)(14, 17, 20), (3, 22, 6, 12)(4, 15)(5, 23, 7, 11)(9, 16, 20, 18)(10, 21, 17, 14)(13, 19), (2, 13, 4, 19)(3, 12, 14, 21)(5, 16, 17, 20)(6, 11, 23, 22)(8, 15)(9, 18), (2, 7, 19, 20, 18, 17, 24)(3, 13, 23, 14, 12, 4, 15)(5, 6, 9, 22, 11, 21, 10), (1, 12, 9, 4)(2, 17, 7, 16)(3, 5)(6, 13, 18, 8)(10, 19)(14, 15, 20, 21), (1, 12, 14, 20, 16, 13, 6, 22, 7, 2, 4, 3, 8, 23)(5, 15)(9, 21, 17, 19, 18, 11, 10), (1, 16, 10, 15, 14, 9, 19, 18, 17, 24)(2, 21, 23, 7, 22, 6, 20, 8, 13, 4)(3, 11)(5, 12) orbits: { 1, 4, 23, 24, 21, 12, 15, 13, 9, 2, 22, 19, 11, 16, 10, 5, 8, 20, 17, 14, 6, 3, 7, 18 }