Some progress on optimal $ 2 $-D $ (n\times m,3,2,1) $-optical orthogonal codes

Kailu Yang; Xiaomiao Wang; Menglong Zhang; Lidong Wang

doi:10.3934/amc.2021012

Article Contents

2023, Volume 17, Issue 3: 605-625. Doi: 10.3934/amc.2021012

This issue Previous Article The weight recursions for the 2-rotation symmetric quartic Boolean functions Next Article Generalized Hamming weights of toric codes over hypersimplices and squarefree affine evaluation codes

Some progress on optimal $ 2 $-D $ (n\times m,3,2,1) $-optical orthogonal codes

1.
School of Mathematics and Statistics, Ningbo University, Ningbo, Zhejiang 315211, China
2.
Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China
3.
School of Intelligence Policing, China People's Police University, Langfang 065000, China

^* Corresponding author: Xiaomiao Wang
^* Corresponding author: Xiaomiao Wang

Received: November 2020

Revised: March 2021

Early access: May 2021

Published: June 2023

This work is supported by Zhejiang Provincial Natural Science Foundation of China under Grant LY21A010005, NSFC under Grant 11771227, the Fundamental Research Funds for the Provincial Universities of Zhejiang under Grant SJLY2020008, and Natural Science Foundation of Ningbo under Grant 202003N4141 (X. Wang), NSFC under Grant 11871095 (M. Zhang), NSFC under Grant 11771119, and NSFHB under Grant A2019507002 (L. Wang).

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Abstract

In this paper, we are concerned about bounds and constructions of optimal $ 2 $-D $ (n\times m,3,2,1) $-optical orthogonal codes. The exact number of codewords of an optimal $ 2 $-D $ (n\times m,3,2,1) $-optical orthogonal code is determined for $ n = 2 $, $ m\equiv 1 \pmod{2} $, and $ n\equiv 1 \pmod{2} $, $ m\equiv 1,3,5 \pmod{12} $, and $ n\equiv 4 \pmod{6} $, $ m\equiv 8 \pmod{16} $.

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Mathematics Subject Classification: Primary: 05B40, 94C30.

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