the 2 isometry classes of irreducible [28,22,4]_2 codes are: code no 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 0 0 0 1 1 0 1 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 1 1 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 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 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 0 1 0 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 1 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 0 1 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 1 0 1 1 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 1 1 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 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 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 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 1 1 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 258048 and is strongly generated by the following 13 elements: ( 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 , 1 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 1 1 0 0 1 0 1 0 1 , 1 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 1 0 1 0 1 0 1 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 1 1 0 0 0 1 1 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 0 1 0 1 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 0 0 1 0 1 0 1 0 1 1 0 , 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 1 1 0 0 0 1 , 0 1 0 1 1 0 1 0 0 1 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 , 1 1 1 0 1 1 0 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 ) acting on the columns of the generator matrix as follows (in order): (6, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28), (6, 20)(18, 19)(21, 24)(22, 23)(25, 28)(26, 27), (5, 17)(6, 24)(11, 16)(12, 15)(13, 14)(18, 23)(19, 22)(20, 21), (5, 15)(6, 22)(11, 14)(12, 17)(13, 16)(18, 21)(19, 24)(20, 23), (5, 22)(6, 15)(11, 21)(12, 24)(13, 23)(14, 18)(16, 20)(17, 19), (5, 18)(6, 11)(12, 20)(13, 19)(14, 22)(15, 21)(16, 24)(17, 23), (4, 9)(5, 14, 12, 16)(6, 21, 19, 23)(8, 10)(11, 15, 13, 17)(18, 22, 20, 24), (4, 8)(5, 21, 11, 22)(6, 14, 18, 15)(9, 10)(12, 23, 13, 24)(16, 20, 17, 19), (4, 21, 14)(5, 6, 25)(8, 22, 15)(9, 23, 16)(10, 24, 17)(11, 18, 26)(12, 19, 27)(13, 20, 28), (3, 7)(4, 8)(5, 21)(6, 15)(11, 22)(12, 24)(13, 23)(14, 18)(16, 19)(17, 20)(25, 26), (2, 7)(4, 8, 9, 10)(5, 11, 12, 13)(6, 20, 19, 18)(15, 17)(21, 23)(25, 27), (1, 5, 8, 15)(2, 11, 4, 14)(3, 12, 10, 17)(6, 22)(7, 13, 9, 16)(18, 21)(19, 24)(20, 23), (1, 4, 28)(2, 10, 26)(3, 8, 25)(5, 14, 20)(6, 12, 15)(7, 9, 27)(11, 17, 18)(13, 16, 19)(21, 22, 23) orbits: { 1, 15, 28, 12, 5, 6, 21, 11, 18, 22, 17, 8, 27, 25, 20, 4, 24, 14, 3, 16, 13, 23, 26, 2, 19, 10, 9, 7 } code no 2: ================ 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 0 0 0 1 1 0 1 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 1 1 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 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 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 0 1 0 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 1 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 0 1 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 1 0 1 1 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 1 1 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 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 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 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 1 1 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 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 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 9216 and is strongly generated by the following 9 elements: ( 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 , 1 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 1 1 0 0 1 0 1 0 1 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 1 0 0 1 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 1 1 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 0 , 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 0 1 0 , 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0 1 1 0 , 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0 1 0 1 1 0 , 0 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 0 0 0 1 0 0 ) acting on the columns of the generator matrix as follows (in order): (5, 17)(6, 24)(11, 16)(12, 15)(13, 14)(18, 23)(19, 22)(20, 21), (5, 15)(6, 22)(11, 14)(12, 17)(13, 16)(18, 21)(19, 24)(20, 23), (5, 21)(6, 14)(11, 22)(12, 23)(13, 24)(15, 18)(16, 19)(17, 20), (5, 24)(6, 17)(11, 23)(12, 22)(13, 21)(14, 20)(15, 19)(16, 18), (3, 7)(4, 8)(5, 22)(6, 14)(11, 21)(12, 23)(13, 24)(15, 18)(16, 20)(17, 19)(25, 26), (3, 4)(5, 18)(6, 11)(7, 8)(12, 22)(13, 21)(14, 20)(15, 19)(16, 24)(17, 23)(27, 28), (2, 7)(4, 9)(5, 22, 12, 24)(6, 17, 19, 15)(11, 23, 13, 21)(14, 20, 16, 18)(25, 27), (2, 7, 8)(3, 9, 4)(5, 18)(6, 13, 21, 11, 19, 15)(12, 24, 14, 20, 16, 22)(17, 23)(25, 27, 28), (1, 21, 4, 6)(2, 22, 8, 18)(3, 23, 9, 19)(5, 14)(7, 24, 10, 20)(11, 15)(12, 16)(13, 17) orbits: { 1, 6, 24, 22, 14, 17, 11, 15, 4, 19, 13, 5, 16, 12, 7, 2, 20, 18, 23, 21, 8, 3, 9, 10 }, { 25, 26, 27, 28 }