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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-4629 2314-4785 |