Optimal conflict-avoiding codes of odd length and weight three

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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