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arXiv · 2009.09601

Revisiting the Factorization of $x^n+1$ over Finite Fields

Arunwan Boripan·Somphong Jitman
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Abstract

The polynomial $x^n+1$ 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 $x^n+1$ over finite fields is given as well as its applications. Explicit and recursive methods for factorizing $x^n+1$ 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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Arunwan Boripan, Somphong Jitman. 2020-09-21. Revisiting the Factorization of $x^n+1$ over Finite Fields. https://arxiv.org/abs/2009.09601

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