Eisenstein field BCH codes construction and decoding
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 investi...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-10-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231508?viewType=HTML |
| _version_ | 1827763163044511744 |
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| author | Muhammad Sajjad Tariq Shah Qin Xin Bander Almutairi |
| author_facet | Muhammad Sajjad Tariq Shah Qin Xin Bander Almutairi |
| author_sort | Muhammad Sajjad |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T10:47:19Z |
| format | Article |
| id | doaj.art-aa37db0d49d8487792624ec55bfb77ae |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-11T10:47:19Z |
| publishDate | 2023-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-aa37db0d49d8487792624ec55bfb77ae2023-11-14T01:30:03ZengAIMS PressAIMS Mathematics2473-69882023-10-01812294532947310.3934/math.20231508Eisenstein field BCH codes construction and decodingMuhammad Sajjad0Tariq Shah 1Qin Xin2Bander Almutairi31. Department of Mathematics, Quaid-I-Azam University, Islamabad 45320, Pakistan1. Department of Mathematics, Quaid-I-Azam University, Islamabad 45320, Pakistan2. Faculty of Science and Technology, University of the Faroe Islands, Faroe Islands, Denmark3. Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaFirst, 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.https://www.aimspress.com/article/doi/10.3934/math.20231508?viewType=HTMLeisenstein integerseisenstein fieldbch codes over eisenstein fieldberlekamp-massey algorithm |
| spellingShingle | Muhammad Sajjad Tariq Shah Qin Xin Bander Almutairi Eisenstein field BCH codes construction and decoding AIMS Mathematics eisenstein integers eisenstein field bch codes over eisenstein field berlekamp-massey algorithm |
| title | Eisenstein field BCH codes construction and decoding |
| title_full | Eisenstein field BCH codes construction and decoding |
| title_fullStr | Eisenstein field BCH codes construction and decoding |
| title_full_unstemmed | Eisenstein field BCH codes construction and decoding |
| title_short | Eisenstein field BCH codes construction and decoding |
| title_sort | eisenstein field bch codes construction and decoding |
| topic | eisenstein integers eisenstein field bch codes over eisenstein field berlekamp-massey algorithm |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231508?viewType=HTML |
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