Two classes of LDPC codes from the space of hermitian matrices over finite fields

Meng Zhao; Changli Ma; Yanan Feng; Qi Wang

doi:10.3934/amc.2022059

Article Contents

2022, Volume 16, Issue 4: 1211-1222. Doi: 10.3934/amc.2022059

This issue Previous Article Constructions of balanced (N, M, {4, 5}, 1;2) Multilength Variable-Weight optical orthogonal codes Next Article

Two classes of LDPC codes from the space of hermitian matrices over finite fields

1.
Department of Mathematics, Southern University of Science and Technology, Shenzhen, Guangdong, China
2.
School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, Hebei, China
3.
Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, Hebei, China
4.
Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, China

^*Corresponding author: Changli Ma
^*Corresponding author: Changli Ma

Received: March 2022

Revised: June 2022

Early access: July 2022

Published: November 2022

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Abstract

For a prime power $ q $, we construct two classes of LDPC codes $ C(n, q^2) $ and $ C^T(n, q^2) $, both with girth $ 8 $, based on the space of $ n\times n $ Hermitian matrices over the finite field $ \mathbb{F}_{q^2} $. The minimum distance and the stopping distance are both determined for $ C^T(n, q^2) $. Meanwhile, lower bounds of these parameters are obtained for $ C(n, q^2) $. Furthermore, when the characteristic of $ \mathbb{F}_{q^2} $ is $ 2 $, we are also able to derive upper bounds of these two parameters for $ C(n, q^2) $.

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Mathematics Subject Classification: Primary: 05B20, 11T71; Secondary: 15B57.

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