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Optimal conflict-avoiding codes of odd length and weight three

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Abstract

A conflict-avoiding code (CAC) \({\mathcal{C}}\) of length n and weight k is a collection of k-subsets of \({\mathbb{Z}_{n}}\) such that \({\Delta (x) \cap \Delta (y) = \emptyset}\) for any \({x, y \in \mathcal{C}}\) , \({x\neq y}\) , where \({\Delta (x) = \{a - b:\,a, b \in x, a \neq b\}}\) . Let CAC(n, k) denote the class of all CACs of length n and weight k. A CAC with maximum size is called optimal. In this paper, we study the constructions of optimal CACs for the case when n is odd and k = 3.

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Authors and Affiliations

  1. Department of Applied Mathematics, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, 30010, Taiwan

    Hung-Lin Fu, Yuan-Hsun Lo & Kenneth W. Shum

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  1. Hung-Lin Fu
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  2. Yuan-Hsun Lo
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  3. Kenneth W. Shum
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Correspondence to Yuan-Hsun Lo.

Additional information

Communicated by V. D. Tonchev.

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Fu, HL., Lo, YH. & Shum, K.W. Optimal conflict-avoiding codes of odd length and weight three. Des. Codes Cryptogr. 72, 289–309 (2014). https://doi.org/10.1007/s10623-012-9764-5

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  • DOI: https://doi.org/10.1007/s10623-012-9764-5

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