the 2 isometry classes of irreducible [17,8,8]_4 codes are: code no 1: ================ 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 3 2 2 2 1 1 1 0 0 0 1 0 0 0 0 0 0 2 3 2 1 2 1 0 1 0 0 0 1 0 0 0 0 0 2 2 3 1 1 2 0 0 1 0 0 0 1 0 0 0 0 3 2 2 1 0 0 2 1 1 0 0 0 0 1 0 0 0 2 3 2 0 1 0 1 2 1 0 0 0 0 0 1 0 0 2 1 3 3 2 1 3 2 1 0 0 0 0 0 0 1 0 1 2 3 2 3 1 2 3 1 0 0 0 0 0 0 0 1 the automorphism group has order 960 and is strongly generated by the following 8 elements: ( 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 2 3 1 1 2 0 0 1 3 1 3 2 3 2 0 2 0 1 3 3 3 2 2 2 0 0 0 0 1 0 0 0 0 0 0 , 0 , 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 , 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 , 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 3 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 3 2 2 1 0 0 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 2 2 2 3 3 3 0 0 0 0 0 0 2 0 0 0 0 , 1 , 2 1 2 0 3 0 3 2 3 1 1 3 2 2 1 0 0 2 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 3 1 2 1 2 0 2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 1 0 0 1 2 3 3 1 2 3 1 2 , 1 , 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 1 2 1 2 3 1 2 3 1 3 2 2 1 3 2 1 3 0 0 0 0 0 0 0 0 1 3 1 3 0 2 0 2 3 2 1 3 3 2 0 0 3 2 2 0 0 0 0 0 3 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 1 1 2 3 3 1 0 0 3 , 0 ) acting on the columns of the generator matrix as follows (in order): (3, 9)(6, 13)(7, 12)(8, 11)(14, 17)(15, 16), (3, 6, 9, 13)(4, 5)(7, 17, 12, 14)(8, 16, 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, 6, 4, 3)(2, 13, 5, 9)(7, 12, 11, 8)(14, 16), (1, 4, 6, 15)(2, 14, 11, 13)(5, 12)(7, 8, 16, 9), (1, 8, 4, 12)(2, 7, 5, 11)(3, 9, 6, 13)(14, 15), (1, 8, 16, 2, 7, 17)(3, 13, 9)(4, 11, 14, 5, 12, 15) orbits: { 1, 3, 15, 12, 17, 9, 13, 6, 8, 4, 16, 11, 14, 7, 2, 5 }, { 10 } code no 2: ================ 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 3 2 2 2 1 1 1 0 0 0 1 0 0 0 0 0 0 2 3 2 1 2 1 0 1 0 0 0 1 0 0 0 0 0 2 2 3 1 1 2 0 0 1 0 0 0 1 0 0 0 0 0 1 2 3 2 0 2 1 1 0 0 0 0 1 0 0 0 1 0 2 2 3 0 1 2 1 0 0 0 0 0 1 0 0 3 0 3 0 1 1 3 2 1 0 0 0 0 0 0 1 0 0 3 3 1 0 1 2 3 1 0 0 0 0 0 0 0 1 the automorphism group has order 16320 and is strongly generated by the following 7 elements: ( 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 0 3 0 2 2 3 1 2 0 3 3 2 0 2 1 3 2 0 0 0 0 0 0 0 0 1 0 0 0 3 0 0 0 0 0 0 0 0 0 3 0 0 0 0 2 2 2 2 2 2 2 2 2 , 1 , 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 1 1 1 3 3 3 0 0 1 2 1 3 1 3 0 3 0 0 0 0 0 0 0 0 0 1 3 0 1 1 2 0 3 1 3 0 3 1 2 1 0 1 3 3 0 0 0 0 0 1 0 0 0 , 0 , 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 3 0 2 2 1 0 3 2 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 3 0 0 0 0 3 0 0 0 0 0 0 2 0 0 0 0 0 0 2 3 3 3 1 1 1 0 0 3 2 3 1 3 1 0 1 0 , 1 , 3 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 2 3 0 3 1 2 3 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 3 0 3 1 2 1 0 1 3 3 3 3 3 3 3 3 3 3 3 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 , 0 , 2 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 0 2 0 3 3 2 1 3 0 2 0 0 0 0 0 0 0 1 0 2 2 3 0 1 2 1 3 3 1 2 2 3 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 3 0 0 0 0 2 3 2 1 2 1 0 1 0 , 0 , 0 0 0 0 0 2 0 0 0 3 2 3 1 3 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 3 0 0 0 0 0 3 3 2 1 1 3 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 , 1 , 0 2 2 1 0 1 3 2 1 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 1 0 3 3 2 0 1 3 1 0 3 0 0 0 0 0 0 0 2 2 1 3 3 2 0 0 3 0 0 0 0 0 0 0 0 2 0 0 0 0 1 0 0 0 0 2 0 2 0 1 1 2 3 1 , 1 ) acting on the columns of the generator matrix as follows (in order): (4, 7, 14, 16)(5, 8, 15, 17)(6, 13, 10, 9)(11, 12), (3, 10)(4, 11)(5, 12)(6, 9)(7, 15)(8, 14), (3, 7, 10, 15)(4, 14, 11, 8)(5, 6, 12, 9)(13, 16), (3, 16, 11, 13, 12, 17)(4, 9, 5, 8, 10, 7)(6, 15, 14), (2, 4, 16, 3, 13, 6)(5, 8, 15)(7, 11, 14, 10, 12, 9), (1, 3, 4, 6)(2, 8, 5, 12)(7, 9, 11, 13)(10, 15), (1, 12, 10, 14, 13, 6, 11, 17)(2, 5, 8, 16, 9, 7, 15, 4) orbits: { 1, 6, 17, 9, 5, 14, 13, 4, 15, 12, 11, 10, 7, 16, 8, 2, 3 }