English

A recurrent construction of irreducible polynomials of fixed degree over finite fields

Number Theory 2020-08-26 v2

Abstract

In this paper we consider in detail the composition of an irreducible polynomial with X^2 and suggest a recurrent construction of irreducible polynomials of fixed degree over finite fields of odd characteristics. More precisely, given an irreducible polynomial of degree n and order 2^rt with t odd, the construction produces ord_t(2)/d irreducible polynomials of degree n and order t for a certain divisor d of n. The construction can be used, for example, to search irreducible polynomials with specific requirements on its coefficients.

Keywords

Cite

@article{arxiv.2005.05285,
  title  = {A recurrent construction of irreducible polynomials of fixed degree over finite fields},
  author = {Gohar M. Kyureghyan and Melsik K. Kyureghyan},
  journal= {arXiv preprint arXiv:2005.05285},
  year   = {2020}
}

Comments

There is an error in the previous version, which is corrected