Revisiting the Factorization of xn+1 over Finite Fields with Applications
The polynomial xn+1 over finite fields has been of interest due to its applications in the study of negacyclic codes over finite fields. In this paper, a rigorous treatment of the factorization of xn+1 over finite fields is given as well as its applications. Explicit and recursive methods for factor...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6626422 |
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| _version_ | 1832560084055490560 |
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| author | Arunwan Boripan Somphong Jitman |
| author_facet | Arunwan Boripan Somphong Jitman |
| author_sort | Arunwan Boripan |
| collection | DOAJ |
| description | The polynomial xn+1 over finite fields has been of interest due to its applications in the study of negacyclic codes over finite fields. In this paper, a rigorous treatment of the factorization of xn+1 over finite fields is given as well as its applications. Explicit and recursive methods for factorizing xn+1 over finite fields are provided together with the enumeration formula. As applications, some families of negacyclic codes are revisited with more clear and simpler forms. |
| format | Article |
| id | doaj-art-0612f05525a94a9ab682485ee430fcb2 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-0612f05525a94a9ab682485ee430fcb22025-02-03T01:28:26ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66264226626422Revisiting the Factorization of xn+1 over Finite Fields with ApplicationsArunwan Boripan0Somphong Jitman1Department of Mathematics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, ThailandDepartment of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom 73000, ThailandThe polynomial xn+1 over finite fields has been of interest due to its applications in the study of negacyclic codes over finite fields. In this paper, a rigorous treatment of the factorization of xn+1 over finite fields is given as well as its applications. Explicit and recursive methods for factorizing xn+1 over finite fields are provided together with the enumeration formula. As applications, some families of negacyclic codes are revisited with more clear and simpler forms.http://dx.doi.org/10.1155/2021/6626422 |
| spellingShingle | Arunwan Boripan Somphong Jitman Revisiting the Factorization of xn+1 over Finite Fields with Applications Journal of Mathematics |
| title | Revisiting the Factorization of xn+1 over Finite Fields with Applications |
| title_full | Revisiting the Factorization of xn+1 over Finite Fields with Applications |
| title_fullStr | Revisiting the Factorization of xn+1 over Finite Fields with Applications |
| title_full_unstemmed | Revisiting the Factorization of xn+1 over Finite Fields with Applications |
| title_short | Revisiting the Factorization of xn+1 over Finite Fields with Applications |
| title_sort | revisiting the factorization of xn 1 over finite fields with applications |
| url | http://dx.doi.org/10.1155/2021/6626422 |
| work_keys_str_mv | AT arunwanboripan revisitingthefactorizationofxn1overfinitefieldswithapplications AT somphongjitman revisitingthefactorizationofxn1overfinitefieldswithapplications |