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Optimal optical orthogonal signature pattern codes with weight three and cross-correlation constraint one

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Abstract

Optical orthogonal signature pattern codes (OOSPCs) have attracted wide attention as signature patterns of spatial optical code division multiple access networks. In this paper, an improved upper bound on the size of an \((m,n,3,\lambda _a,1)\)-OOSPC with \(\lambda _a=2,3\) is established. The exact number of codewords of an optimal \((m,n,3,\lambda _a,1)\)-OOSPC is determined for any positive integers \(m,n\equiv 2\ ({\mathrm{mod }}\ 4)\) and \(\lambda _a\in \{2,3\}\).

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Authors and Affiliations

  1. Department of Mathematics, Yunnan University, Kunming, 650504, People’s Republic of China

    Rong Pan

  2. Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    Tao Feng

  3. Department of Basic Courses, China People’s Police University, Langfang, 065000, People’s Republic of China

    Lidong Wang

  4. School of Mathematics and Statistics, Ningbo University, Ningbo, 315211, People’s Republic of China

    Xiaomiao Wang

Authors
  1. Rong Pan
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  2. Tao Feng
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  3. Lidong Wang
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  4. Xiaomiao Wang
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Corresponding author

Correspondence to Xiaomiao Wang.

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Communicated by M. Buratti.

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Supported by NSFC under Grant 11601472, and the Yunnan Applied Basic Research Project of China under Grant 2016FD005 (R. Pan), NSFC under Grant 11871095, and Fundamental Research Funds for the Central Universities under Grant 2016JBZ012 (T. Feng), NSFC under Grant 11771119, and NSFHB under Grant A2019507002 (L. Wang), NSFC under Grants 11771227, 11871291, and Zhejiang Provincial Natural Science Foundation of China under Grant LY17A010008 (X. Wang).

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Pan, R., Feng, T., Wang, L. et al. Optimal optical orthogonal signature pattern codes with weight three and cross-correlation constraint one. Des. Codes Cryptogr. 88, 119–131 (2020). https://doi.org/10.1007/s10623-019-00675-0

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  • DOI: https://doi.org/10.1007/s10623-019-00675-0

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