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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Bibliographic Details
Published in:Journal of mathematics (Hidawi) 2021, Vol.2021
Main Authors: Boripan, Arunwan, Jitman, Somphong
Format: Article
Language:English
Subjects:
Binary system
Codes
Enumeration
Factorization
Fields (mathematics)
Mathematics
Polynomials
Recursive methods
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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.
ISSN:2314-4629
2314-4785
DOI:10.1155/2021/6626422