Structure and Rank of a Cyclic Code over a Class of Nonchain Rings
The rings Z4+νZ4 have been classified into chain rings and nonchain rings based on the values of ν2∈Z4+νZ4. In this paper, the structure of a cyclic code of arbitrary length over the rings Z4+νZ4 for those values of ν2 for which these are nonchain rings has been established. A unique form of generat...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2024-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/8817721 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832548328846393344 |
|---|---|
| author | Nikita Jain Sucheta Dutt Ranjeet Sehmi |
| author_facet | Nikita Jain Sucheta Dutt Ranjeet Sehmi |
| author_sort | Nikita Jain |
| collection | DOAJ |
| description | The rings Z4+νZ4 have been classified into chain rings and nonchain rings based on the values of ν2∈Z4+νZ4. In this paper, the structure of a cyclic code of arbitrary length over the rings Z4+νZ4 for those values of ν2 for which these are nonchain rings has been established. A unique form of generators for a cyclic code over these rings has also been obtained. Furthermore, the rank and cardinality of a cyclic code over these rings have been established by finding a minimal spanning set for the code. |
| format | Article |
| id | doaj-art-5f1a16e512e3465f9846f3db427570a5 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-5f1a16e512e3465f9846f3db427570a52025-02-03T06:14:53ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/8817721Structure and Rank of a Cyclic Code over a Class of Nonchain RingsNikita Jain0Sucheta Dutt1Ranjeet Sehmi2Department of MathematicsDepartment of MathematicsDepartment of MathematicsThe rings Z4+νZ4 have been classified into chain rings and nonchain rings based on the values of ν2∈Z4+νZ4. In this paper, the structure of a cyclic code of arbitrary length over the rings Z4+νZ4 for those values of ν2 for which these are nonchain rings has been established. A unique form of generators for a cyclic code over these rings has also been obtained. Furthermore, the rank and cardinality of a cyclic code over these rings have been established by finding a minimal spanning set for the code.http://dx.doi.org/10.1155/2024/8817721 |
| spellingShingle | Nikita Jain Sucheta Dutt Ranjeet Sehmi Structure and Rank of a Cyclic Code over a Class of Nonchain Rings Journal of Mathematics |
| title | Structure and Rank of a Cyclic Code over a Class of Nonchain Rings |
| title_full | Structure and Rank of a Cyclic Code over a Class of Nonchain Rings |
| title_fullStr | Structure and Rank of a Cyclic Code over a Class of Nonchain Rings |
| title_full_unstemmed | Structure and Rank of a Cyclic Code over a Class of Nonchain Rings |
| title_short | Structure and Rank of a Cyclic Code over a Class of Nonchain Rings |
| title_sort | structure and rank of a cyclic code over a class of nonchain rings |
| url | http://dx.doi.org/10.1155/2024/8817721 |
| work_keys_str_mv | AT nikitajain structureandrankofacycliccodeoveraclassofnonchainrings AT suchetadutt structureandrankofacycliccodeoveraclassofnonchainrings AT ranjeetsehmi structureandrankofacycliccodeoveraclassofnonchainrings |