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arXiv · 2610.30003

On optimal (v,5,3,1) optical orthogonal codes

Laura Johnson·Lorenzo Mella·Anita Pasotti·Emma Smith
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Abstract

In this paper, we establish a tight upper bound for the size of a $(v,5,3,1)$ optical orthogonal code (OOC) and call such a code optimal when it achieves this upper bound. In addition, if an optimal OOC has the property that all non-identity elements of $\mathbb{Z}_v$ are covered by the list of differences of its codeword-sets then it is called perfect. In this paper, we present direct and recursive constructions for infinite classes of optimal and perfect $(v,5,3,1)$-OOCs.

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Laura Johnson, Lorenzo Mella, Anita Pasotti, Emma Smith. 2026-10-21. On optimal (v,5,3,1) optical orthogonal codes. https://arxiv.org/abs/2610.30003

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