A Family of Almost MDS Symbol-Pair Codes of Length 8p
In high-density data storage systems, symbol-pair codes are commonly used to prevent symbol-pair errors. Designing maximum distance separable (MDS) codes is crucial in symbol-pair coding theory because MDS symbol-pair codes are the best at meeting the Singleton bound, which is a measure of their eff...
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IEEE
2025-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/11084795/ |
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| author | Hai Q. Dinh Bac T. Nguyen Hiep L. Thi Woraphon Yamaka |
| author_facet | Hai Q. Dinh Bac T. Nguyen Hiep L. Thi Woraphon Yamaka |
| author_sort | Hai Q. Dinh |
| collection | DOAJ |
| description | In high-density data storage systems, symbol-pair codes are commonly used to prevent symbol-pair errors. Designing maximum distance separable (MDS) codes is crucial in symbol-pair coding theory because MDS symbol-pair codes are the best at meeting the Singleton bound, which is a measure of their effectiveness. However, obtaining MDS codes is challenging due to the difficulty of meeting the strict requirements of the Singleton bound. As an alternative, almost maximum distance separable (AMDS) symbol-pair codes are explored since they are not as perfect as MDS codes according to the Singleton bound. In this paper, we introduce a new family of AMDS symbol-pair cyclic codes of length <inline-formula> <tex-math notation="LaTeX">$8p$ </tex-math></inline-formula> for every prime number <inline-formula> <tex-math notation="LaTeX">$p \equiv 1 \mod 8$ </tex-math></inline-formula>. This results in a useful collection of AMDS symbol-pair cyclic codes applicable directly in various real-world scenarios. |
| format | Article |
| id | doaj-art-fd3bd397d84041e789ae6dc81483591f |
| institution | Kabale University |
| issn | 2169-3536 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj-art-fd3bd397d84041e789ae6dc81483591f2025-08-20T03:41:52ZengIEEEIEEE Access2169-35362025-01-011313907113907910.1109/ACCESS.2025.359046211084795A Family of Almost MDS Symbol-Pair Codes of Length 8pHai Q. Dinh0Bac T. Nguyen1https://orcid.org/0000-0001-6637-4185Hiep L. Thi2Woraphon Yamaka3Faculty of Data Science in Business, Ho Chi Minh University of Banking, Ho Chi Minh City, VietnamInstitute of Fundamental and Applied Sciences, Duy Tan University, Ho Chi Minh City, VietnamFaculty of Education, Thu Dau Mot University, Thu Dau Mot, Binh Duong, VietnamCentre of Excellence in Econometrics, Chiang Mai University, Chiang Mai, ThailandIn high-density data storage systems, symbol-pair codes are commonly used to prevent symbol-pair errors. Designing maximum distance separable (MDS) codes is crucial in symbol-pair coding theory because MDS symbol-pair codes are the best at meeting the Singleton bound, which is a measure of their effectiveness. However, obtaining MDS codes is challenging due to the difficulty of meeting the strict requirements of the Singleton bound. As an alternative, almost maximum distance separable (AMDS) symbol-pair codes are explored since they are not as perfect as MDS codes according to the Singleton bound. In this paper, we introduce a new family of AMDS symbol-pair cyclic codes of length <inline-formula> <tex-math notation="LaTeX">$8p$ </tex-math></inline-formula> for every prime number <inline-formula> <tex-math notation="LaTeX">$p \equiv 1 \mod 8$ </tex-math></inline-formula>. This results in a useful collection of AMDS symbol-pair cyclic codes applicable directly in various real-world scenarios.https://ieeexplore.ieee.org/document/11084795/Symbol-pair distancecyclic codeMDS codeAMDS code |
| spellingShingle | Hai Q. Dinh Bac T. Nguyen Hiep L. Thi Woraphon Yamaka A Family of Almost MDS Symbol-Pair Codes of Length 8p IEEE Access Symbol-pair distance cyclic code MDS code AMDS code |
| title | A Family of Almost MDS Symbol-Pair Codes of Length 8p |
| title_full | A Family of Almost MDS Symbol-Pair Codes of Length 8p |
| title_fullStr | A Family of Almost MDS Symbol-Pair Codes of Length 8p |
| title_full_unstemmed | A Family of Almost MDS Symbol-Pair Codes of Length 8p |
| title_short | A Family of Almost MDS Symbol-Pair Codes of Length 8p |
| title_sort | family of almost mds symbol pair codes of length 8p |
| topic | Symbol-pair distance cyclic code MDS code AMDS code |
| url | https://ieeexplore.ieee.org/document/11084795/ |
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