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PreprintCC BY 4.0arXiv

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 ℤv 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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Cite

BibTeXRIS
BibTeX
@misc{johnson2026optimal,
  title = {{On optimal (v,5,3,1) optical orthogonal codes}},
  author = {Laura Johnson and Lorenzo Mella and Anita Pasotti and Emma Smith},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30003},
  eprint = {2610.30003},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30003},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On optimal (v,5,3,1) optical orthogonal codes
AU  - Laura Johnson
AU  - Lorenzo Mella
AU  - Anita Pasotti
AU  - Emma Smith
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.30003
UR  - https://arxiv.org/abs/2610.30003
AB  - 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 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.
ER  -