the 1 isometry classes of irreducible [18,9,8]_4 codes are: code no 1: ================ 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 3 2 2 2 1 1 1 0 0 0 1 0 0 0 0 0 0 0 2 3 2 1 2 1 0 1 0 0 0 1 0 0 0 0 0 0 2 2 3 1 1 2 0 0 1 0 0 0 1 0 0 0 0 0 3 2 2 1 0 0 2 1 1 0 0 0 0 1 0 0 0 0 2 3 2 0 1 0 1 2 1 0 0 0 0 0 1 0 0 0 2 1 3 3 2 1 3 2 1 0 0 0 0 0 0 1 0 0 1 2 3 2 3 1 2 3 1 0 0 0 0 0 0 0 1 0 1 1 2 0 0 3 3 3 1 0 0 0 0 0 0 0 0 1 the automorphism group has order 16320 and is strongly generated by the following 8 elements: ( 1 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 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 , 0 , 3 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 3 1 1 1 2 2 2 0 0 1 3 1 2 1 2 0 2 0 1 1 3 2 2 1 0 0 2 3 1 1 2 0 0 1 2 2 1 3 1 0 2 0 2 1 2 1 1 3 0 0 2 2 2 1 , 1 , 3 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 2 2 1 3 3 2 0 0 3 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 3 1 1 2 0 0 1 2 2 1 3 1 0 2 0 2 1 2 0 0 0 0 0 1 0 0 0 , 1 , 3 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 3 2 2 1 3 2 1 3 0 0 0 0 0 0 0 2 0 1 1 2 3 3 1 0 0 3 1 2 1 0 3 0 3 1 3 0 0 0 0 2 0 0 0 0 1 1 2 0 0 3 3 3 1 1 2 1 3 1 3 0 3 0 , 0 , 2 0 0 0 0 0 0 0 0 2 3 3 1 0 0 3 1 1 0 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3 2 3 0 1 0 1 3 1 1 3 1 2 1 2 0 2 0 1 2 3 3 1 2 3 1 2 1 2 2 2 3 3 3 0 0 , 1 , 3 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 1 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 3 0 0 1 3 2 2 1 3 2 1 3 3 2 2 1 0 0 2 1 1 3 2 2 2 1 1 1 0 0 , 0 , 3 2 3 1 3 1 0 1 0 2 3 3 3 1 1 1 0 0 3 3 2 1 1 3 0 0 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 1 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 , 3 3 2 0 0 1 1 1 3 2 3 1 1 2 3 1 2 3 0 0 0 0 0 0 3 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 3 0 0 2 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 3 2 3 0 1 0 1 3 1 , 1 ) acting on the columns of the generator matrix as follows (in order): (4, 7)(5, 8)(6, 9)(11, 14)(12, 15)(13, 18), (4, 14, 7, 11)(5, 15, 8, 12)(6, 18, 9, 13)(16, 17), (3, 6, 9, 13)(4, 5)(7, 17, 12, 14)(8, 16, 11, 15), (3, 17, 16)(4, 13, 5, 7, 18, 8)(6, 14, 12, 9, 11, 15), (2, 12, 7, 14)(3, 4, 15, 6)(5, 13, 16, 8)(9, 11), (2, 4, 5)(3, 14, 8)(6, 16, 7)(9, 17, 11)(12, 13, 15), (1, 8, 4, 12)(2, 7, 5, 11)(3, 9, 6, 13)(14, 15), (1, 17, 14, 15, 9, 6, 16, 2, 12, 11, 13, 18)(3, 7)(4, 8, 5) orbits: { 1, 12, 18, 15, 8, 17, 14, 2, 4, 13, 6, 7, 5, 11, 16, 3, 9 }, { 10 }