Constructions for optimal cyclic ternary constant-weight codes of weight four and distance six

摘要

A cyclic (n, d, w)(q) code is a q-ary cyclic code of length n, minimum Hamming distance d and weight w. In this paper, we investigate cyclic (n, 6, 4)(3) codes. A new upper bound on CA(3)(n, 6, 4), the largest possible number of codewords in a cyclic (n, 6, 4)(3) code, is given. Two new constructions for optimal cyclic (n, 6, 4)(3) codes based on cyclic (n, 4, 1) difference packings are presented. As a consequence, the exact value of CA(3)(n, 6, 4) is determined for any positive integer n 0, 6, 18 (mod 24). We also obtain some other infinite classes of optimal cyclic (n, 6, 4)(3) codes. (C) 2018 Elsevier B.V. All rights reserved.