MDS and MHDR Cyclic Codes over Finite Chain Rings

Monika Dalal, Sucheta Dutt, Ranjeet Sehmi and Xiaogang Liu

Journal of Mathematics, 2024, vol. 2024, 1-8

Abstract: This work establishes a unique set of generators for a cyclic code over a finite chain ring. Towards this, we first determine the minimal spanning set and rank of the code. Furthermore, sufficient as well as necessary conditions for a cyclic code to be an MDS code and for a cyclic code to be an MHDR code are obtained. Finally, to support our results, some examples of optimal cyclic codes are presented.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:4540992

DOI: 10.1155/2024/4540992

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