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The sizes of maximal \((v,k,k-2,k-1)\) optical orthogonal codes

  • Zenghui Fang
  • Junling ZhouEmail author
Article
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Abstract

An optical orthogonal code (OOC) is a family of binary sequences having good auto- and cross-correlation properties. Let \(\Phi (v,k,\lambda _{a},\lambda _{c})\) denote the largest possible size among all \((v,k,\lambda _{a},\lambda _{c})\)-OOCs. A \((v,k,\lambda _{a},\lambda _{c})\)-OOC with \(\Phi (v,k,\lambda _{a},\lambda _{c})\) codewords is said to be maximal. In this paper, we research into maximal \((v,k,k-2,k-1)\)-OOCs and determine the exact value of \(\Phi (v,k,k-2,k-1)\). This generalizes the result on the special case of \(k=4\) by Huang and Chang in 2012. Distributions of differences with maximum multiplicity are analyzed by several classes to deal with the general case for all possible v and k.

Keywords

List of differences Maximal Optical orthogonal code Orbit Stabilizer 

Mathematics Subject Classification

05B30 94B65 94C30 

Notes

Acknowledgements

The authors would like to thank Prof. Yanxun Chang for many valuable suggestions and comments. They also wish to thank Prof. Marco Buratti and two anonymous referees for carefully reading the manuscript and suggesting several corrections and improvements.

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© Springer Science+Business Media, LLC, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Department of MathematicsBeijing Jiaotong UniversityBeijingPeople’s Republic of China

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