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

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 CA3(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 CA3(n,6,4) is determined for any positive integer n≡0,6,18(mod24). We also obtain some other infinite classes of optimal cyclic (n,6,4)3 codes.