Revisiting the Factorization of $x^n+1$ over Finite Fields
Number Theory
2020-09-22 v1 Rings and Algebras
Abstract
The polynomial 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 over finite fields is given as well as its applications. Explicit and recursive methods for factorizing 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.
Keywords
Cite
@article{arxiv.2009.09601,
title = {Revisiting the Factorization of $x^n+1$ over Finite Fields},
author = {Arunwan Boripan and Somphong Jitman},
journal= {arXiv preprint arXiv:2009.09601},
year = {2020}
}