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

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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.

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Authors and Affiliations

  1. Department of Information Science, Gifu University, 1-1 Yanagido, Gifu, 501-1193, Japan

    Miwako Mishima

  2. Department of Applied Mathematics, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, 30050, Taiwan

    Hung-Lin Fu

  3. Makita Corporation, 3-11-8 Sumiyoshi, Anjyo, Aichi, 446-8502, Japan

    Shoichi Uruno

Authors
  1. Miwako Mishima
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  2. Hung-Lin Fu
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  3. Shoichi Uruno
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Correspondence to Miwako Mishima.

Additional information

Communicated by V.D. Tonchev.

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Mishima, M., Fu, HL. & Uruno, S. Optimal conflict-avoiding codes of length n ≡ 0 (mod 16) and weight 3. Des. Codes Cryptogr. 52, 275–291 (2009). https://doi.org/10.1007/s10623-009-9282-2

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  • DOI: https://doi.org/10.1007/s10623-009-9282-2

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