MDS and MHDR Cyclic Codes over Finite Chain Rings
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...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2024-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/4540992 |
| _version_ | 1797335558840647680 |
|---|---|
| author | Monika Dalal Sucheta Dutt Ranjeet Sehmi |
| author_facet | Monika Dalal Sucheta Dutt Ranjeet Sehmi |
| author_sort | Monika Dalal |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T08:39:58Z |
| format | Article |
| id | doaj.art-10b1581477ea4955bdc3427379b69bc6 |
| institution | Directory Open Access Journal |
| issn | 2314-4785 |
| language | English |
| last_indexed | 2024-03-08T08:39:58Z |
| publishDate | 2024-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj.art-10b1581477ea4955bdc3427379b69bc62024-02-02T00:00:05ZengHindawi LimitedJournal of Mathematics2314-47852024-01-01202410.1155/2024/4540992MDS and MHDR Cyclic Codes over Finite Chain RingsMonika Dalal0Sucheta Dutt1Ranjeet Sehmi2Department of Applied SciencesDepartment of Applied SciencesDepartment of Applied SciencesThis 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.http://dx.doi.org/10.1155/2024/4540992 |
| spellingShingle | Monika Dalal Sucheta Dutt Ranjeet Sehmi MDS and MHDR Cyclic Codes over Finite Chain Rings Journal of Mathematics |
| title | MDS and MHDR Cyclic Codes over Finite Chain Rings |
| title_full | MDS and MHDR Cyclic Codes over Finite Chain Rings |
| title_fullStr | MDS and MHDR Cyclic Codes over Finite Chain Rings |
| title_full_unstemmed | MDS and MHDR Cyclic Codes over Finite Chain Rings |
| title_short | MDS and MHDR Cyclic Codes over Finite Chain Rings |
| title_sort | mds and mhdr cyclic codes over finite chain rings |
| url | http://dx.doi.org/10.1155/2024/4540992 |
| work_keys_str_mv | AT monikadalal mdsandmhdrcycliccodesoverfinitechainrings AT suchetadutt mdsandmhdrcycliccodesoverfinitechainrings AT ranjeetsehmi mdsandmhdrcycliccodesoverfinitechainrings |