Eisenstein field BCH codes construction and decoding

Muhammad Sajjad; Tariq Shah; Qin Xin; Bander Almutairi; Muhammad Sajjad; Tariq Shah; Qin Xin; Bander Almutairi

doi:10.3934/math.20231508

AIMS Mathematics

2023, Volume 8, Issue 12: 29453-29473. doi: 10.3934/math.20231508

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Research article Special Issues

Eisenstein field BCH codes construction and decoding

1.
Department of Mathematics, Quaid-I-Azam University, Islamabad 45320, Pakistan
2.
Faculty of Science and Technology, University of the Faroe Islands, Faroe Islands, Denmark
3.
Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 26 July 2023 Revised: 14 September 2023 Accepted: 18 September 2023 Published: 31 October 2023
MSC : 11T71, 81P73, 94Bxx

First, we will go through the theory behind the Eisenstein field (EF) and its extension field. In contrast, we provide a detailed framework for building BCH codes over the EF in the second stage. BCH codes over the EF are decoded using the Berlekamp-Massey algorithm (BMA) in this article. We investigate the error-correcting capabilities of these codes and provide expressions for minimal distance. We provide researchers and engineers creating and implementing robust error-correcting codes for digital communication systems with detailed information on building, decoding and performance assessment.
- Eisenstein integers,
- Eisenstein field,
- BCH codes over Eisenstein field,
- Berlekamp-Massey algorithm
Citation: Muhammad Sajjad, Tariq Shah, Qin Xin, Bander Almutairi. Eisenstein field BCH codes construction and decoding[J]. AIMS Mathematics, 2023, 8(12): 29453-29473. doi: 10.3934/math.20231508

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Abstract

First, we will go through the theory behind the Eisenstein field (EF) and its extension field. In contrast, we provide a detailed framework for building BCH codes over the EF in the second stage. BCH codes over the EF are decoded using the Berlekamp-Massey algorithm (BMA) in this article. We investigate the error-correcting capabilities of these codes and provide expressions for minimal distance. We provide researchers and engineers creating and implementing robust error-correcting codes for digital communication systems with detailed information on building, decoding and performance assessment.

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