Optimal conflict-avoiding codes of odd length and weight three

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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.