English

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

Number Theory 2020-09-22 v1 Rings and Algebras

Abstract

The polynomial xn+1x^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 xn+1x^n+1 over finite fields is given as well as its applications. Explicit and recursive methods for factorizing xn+1x^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.

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}
}