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