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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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
IEEE
2025-01-01
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| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/11084795/ |
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| Summary: | 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. |
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| ISSN: | 2169-3536 |