the 3 isometry classes of irreducible [27,24,3]_5 codes are: code no 1: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 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 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 800 and is strongly generated by the following 5 elements: ( 3 0 0 0 1 0 0 0 1 , 3 0 0 0 4 0 0 2 2 , 3 0 0 1 2 4 1 4 2 , 2 0 0 4 4 2 4 0 1 , 0 2 3 2 1 1 3 1 1 ) acting on the columns of the generator matrix as follows (in order): (4, 14, 16, 15)(5, 6, 8, 7)(9, 10, 12, 11)(18, 19, 21, 20)(23, 24, 26, 25), (3, 17, 22, 13)(4, 12, 18, 26)(5, 7, 8, 6)(9, 21, 23, 16)(10, 20, 24, 15)(11, 19, 25, 14), (2, 21, 12, 26)(3, 24, 8, 20)(4, 15, 14, 13)(5, 17, 11, 23)(6, 18, 10, 25)(7, 19, 9, 22), (2, 21, 6, 19)(3, 11, 10, 12)(4, 25, 15, 22)(5, 20)(7, 18, 8, 17)(13, 24, 16, 23)(14, 26), (1, 27)(2, 4, 22, 15, 3, 16, 17, 14)(5, 7, 24, 23, 12, 10, 18, 20)(6, 21, 26, 8, 11, 25, 19, 9) orbits: { 1, 27 }, { 2, 26, 19, 14, 24, 18, 12, 21, 11, 7, 6, 25, 4, 15, 17, 23, 20, 3, 13, 10, 9, 8, 5, 22, 16 } code no 2: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 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 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 24 and is strongly generated by the following 5 elements: ( 4 0 0 2 3 3 2 4 2 , 2 0 0 2 1 3 2 4 0 , 4 0 0 1 2 2 2 1 3 , 0 3 2 3 4 2 0 4 2 , 1 4 1 0 0 2 4 0 2 ) acting on the columns of the generator matrix as follows (in order): (2, 16)(3, 18)(4, 8)(5, 14)(6, 13)(7, 15)(9, 20)(10, 17)(11, 19)(12, 21)(22, 25)(23, 24), (2, 12, 16, 21)(3, 15, 18, 7)(4, 17, 8, 10)(5, 9, 14, 20)(6, 11, 13, 19)(22, 23, 25, 24), (2, 15)(3, 21)(4, 8)(5, 13)(6, 14)(7, 16)(9, 19)(10, 17)(11, 20)(12, 18)(26, 27), (1, 26)(2, 12, 16, 21)(3, 10, 18, 17)(4, 7, 8, 15)(5, 23, 14, 24)(6, 19, 13, 11)(9, 25, 20, 22), (1, 26, 27)(2, 4, 15, 12, 17, 18, 16, 8, 7, 21, 10, 3)(5, 11, 22, 9, 13, 23, 14, 19, 25, 20, 6, 24) orbits: { 1, 26, 27 }, { 2, 16, 21, 15, 3, 12, 7, 18, 8, 4, 17, 10 }, { 5, 14, 20, 13, 24, 9, 6, 23, 11, 25, 19, 22 } code no 3: ================ 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 0 4 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 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 2 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 the automorphism group has order 24 and is strongly generated by the following 4 elements: ( 3 0 0 0 3 0 4 4 2 , 1 0 0 0 4 0 0 2 1 , 1 0 0 2 2 2 2 1 3 , 1 1 1 3 0 0 1 0 4 ) acting on the columns of the generator matrix as follows (in order): (3, 19)(9, 18)(10, 17)(11, 21)(12, 20)(13, 14)(15, 16)(22, 27)(23, 26)(24, 25), (3, 17)(5, 8)(6, 7)(9, 18)(10, 19)(11, 20)(12, 21)(22, 25)(23, 26)(24, 27), (2, 4)(3, 21)(5, 16)(6, 14)(7, 13)(8, 15)(9, 18)(10, 20)(11, 17)(12, 19)(22, 24), (1, 2, 4)(3, 22, 12)(5, 23, 16)(6, 9, 13)(7, 18, 14)(8, 26, 15)(10, 25, 20)(11, 17, 27)(19, 24, 21) orbits: { 1, 4, 2 }, { 3, 19, 17, 21, 12, 10, 11, 24, 20, 22, 27, 25 }, { 5, 8, 16, 15, 23, 26 }, { 6, 7, 14, 13, 18, 9 }