the 2 isometry classes of irreducible [18,15,4]_16 codes are: code no 1: ================ 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 8 4 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 9 5 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 13 6 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 12 7 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 14 8 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 15 9 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 7 10 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 6 11 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 11 12 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 10 13 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 4 14 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 5 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 144 and is strongly generated by the following 6 elements: ( 1 0 0 0 1 0 1 1 1 , 0 , 13 0 0 0 13 0 7 5 13 , 2 , 3 0 0 0 3 0 11 1 3 , 3 , 15 12 2 2 14 7 5 10 13 , 1 , 10 7 2 10 10 10 0 13 0 , 0 , 5 5 5 5 15 1 5 8 9 , 0 ) acting on the columns of the generator matrix as follows (in order): (3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18), (3, 9, 4, 10)(5, 18, 6, 17)(7, 11, 8, 12)(13, 15, 14, 16), (3, 11, 10, 7, 4, 12, 9, 8)(5, 15, 17, 13, 6, 16, 18, 14), (1, 6, 15, 5, 17, 13, 14, 16)(2, 10, 8, 9, 3, 11, 12, 7), (1, 17, 18)(2, 3, 4)(5, 13, 15)(6, 16, 14)(7, 12, 10)(8, 9, 11), (1, 10, 14, 4)(2, 6, 12, 18)(3, 5, 7, 15)(8, 17, 9, 16)(11, 13) orbits: { 1, 16, 18, 4, 15, 14, 6, 9, 17, 5, 12, 3, 7, 13, 10, 2, 8, 11 } code no 2: ================ 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 5 3 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 2 4 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 12 5 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 14 6 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 10 7 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 11 8 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 13 9 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 9 10 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 6 11 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 8 12 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 4 13 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 15 14 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 7 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 16320 and is strongly generated by the following 6 elements: ( 5 0 0 0 15 0 0 0 8 , 2 , 4 0 0 0 1 0 0 0 14 , 1 , 5 0 0 0 8 0 13 12 7 , 3 , 9 0 0 0 10 0 9 10 12 , 1 , 4 0 0 7 15 10 4 11 7 , 2 , 12 2 14 2 13 4 1 2 12 , 0 ) acting on the columns of the generator matrix as follows (in order): (4, 6)(7, 14)(8, 11)(9, 12)(10, 13)(15, 17), (4, 17, 6, 15)(7, 8, 14, 11)(9, 10, 12, 13)(16, 18), (3, 16)(4, 7, 6, 14)(8, 13, 11, 10)(9, 15, 12, 17), (3, 4, 11, 10)(6, 14, 16, 8)(7, 13)(9, 12, 17, 18), (2, 6, 16, 10, 3, 15)(4, 14, 13, 12, 17, 8)(7, 11, 9), (1, 7, 3, 12, 17)(2, 16, 6, 14, 8)(4, 11, 15, 13, 9) orbits: { 1, 17, 15, 4, 12, 6, 9, 3, 11, 14, 8, 10, 13, 7, 2, 16, 18 }, { 5 }