Constructions of optimal balanced $ (m, n, \{4, 5\}, 1) $-OOSPCs

Wei Li; Hengming Zhao; Rongcun Qin; Dianhua Wu

doi:10.3934/amc.2019022

Article Contents

2019, Volume 13, Issue 2: 329-341. Doi: 10.3934/amc.2019022

This issue Previous Article Symmetries of weight enumerators and applications to Reed-Muller codes Next Article Efficient public-key operation in multivariate schemes

Constructions of optimal balanced $ (m, n, \{4, 5\}, 1) $-OOSPCs

1.
Faculty of Engineering, Information and Systems, University of Tsukuba, Tsukuba 305-8573, Japan
2.
Xingjian College of Science and Liberal Arts, Guangxi University, Nanning 530004, China
3.
Guangxi Key Lab of Multi-source Information Mining & Security, Department of Mathematics, Guangxi Normal University, Guilin 541004, China

^* Corresponding author: Dianhua Wu
^* Corresponding author: Dianhua Wu

Received: June 2018

Published: January 2019

The second author is supported in part by Guangxi Nature Science Foundation (No. 2018GXNSFA138038). The third author is supported by the Project of Basic Ability Improvement of Young and Middle-Aged Teachers of Universities in Guangxi (No. 2017KY1301). The last author is supported in part by NSFC (No. 11671103, 11801103), Guangxi Nature Science Foundation (No. 2017GXNSFBA198030), and Foundation of Guangxi Key Lab of Multi-Source Information Mining and Security (No. 18-A-03-01)

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Abstract

Kitayama proposed a novel OCDMA (called spatial CDMA) for parallel transmission of 2-D images through multicore fiber. Optical orthogonal signature pattern codes (OOSPCs) play an important role in this CDMA network. Multiple-weight (MW) optical orthogonal signature pattern code (OOSPC) was introduced by Kwong and Yang for 2-D image transmission in multicore-fiber optical code-division multiple-access (OCDMA) networks with multiple quality of services (QoS) requirements. Some results had been done on optimal balanced $ (m, n, \{3, 4\}, 1) $-OOSPCs. In this paper, it is proved that there exist optimal balanced $ (2u, 16v, \{4, 5\}, 1) $-OOSPCs for odd integers $ u\geq 1 $, $ v\geq 1 $.

Keywords:

Incomplete difference matrix,
optical orthogonal signature pattern code,
optimal,
packing,
quadratic residue.

Mathematics Subject Classification: Primary: 05B40; Secondary: 94C30.

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References

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