New optimal (v, k, 1) optical orthogonal codes with k = 3, 5, 6
DOI:
https://doi.org/10.55630/mem.2026.55.329-339Keywords:
coding theory, optimal optical orthogonal code, binary cyclically permutable constant weight code, cyclic difference family, cyclic designAbstract
The known classifications of optimal optical orthogonal codes with small k show that when the code length v grows, the number of nonequivalent codes increases very fast. This either makes the complete classification for relatively big values of v infeasible, or the number of the obtained codes is so big that it is very difficult to choose among them a code with the properties you need. That is why in the present work we do not obtain all the codes with the considered parameters. We construct sets of new optimal (v, k, 1) optical orthogonal codes with k = 3, 5, and 6 for relatively small values of the code lengths v for which no classification results are known. The codes in each of these sets differ from one another in many codewords. They can be used in practical applications, as well as in further research on the topic.
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