Revisiting the Factorization of xn+1 over Finite Fields with Applications

Arunwan Boripan, Somphong Jitman and Marco Fontana

Journal of Mathematics, 2021, vol. 2021, 1-10

Abstract: 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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6626422

DOI: 10.1155/2021/6626422

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