Optimal conflict-avoiding codes of length n equivalent to 0 (mod 16) and weight 3

Abstract

A conflict-avoiding code of length n and weight k is defined as a set C subset of {0, 1}(n) of binary vectors, called codewords, all of Hamming weight k such that the distance of arbitrary cyclic shifts of two distinct codewords in C is at least 2k - 2. In this paper, we obtain direct constructions for optimal conflict-avoiding codes of length n = 16m and weight 3 for any m by utilizing Skolem type sequences. We also show that for the case n = 16m + 8 Skolem type sequences can give more concise constructions than the ones obtained earlier by Jimbo et al.