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

Authors:
Miwako Mishima;Hung-Lin Fu;Shoichi Uruno
Affiliations:
Department of Information Science, Gifu University, Gifu, Japan 501-1193;Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan 30050;Makita Corporation, Anjyo, Aichi, Japan 446-8502
Venue:
Designs, Codes and Cryptography
Year:
2009

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Abstract

A conflict-avoiding code of length n and weight k is defined as a set $${C \subseteq \{0,1\}^n}$$ 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.