, Volume 72, Issue 2, pp 289-309
Date: 07 Nov 2012

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.

Communicated by V. D. Tonchev.