Recursive construction of primitive polynomials over finite fields

TL;DR

This paper presents a straightforward recursive method for constructing sequences of primitive polynomials over finite fields, which are essential for applications in coding theory and cryptography.

Contribution

It introduces a new explicit recursive approach for generating primitive polynomials of degrees that are powers of two over finite fields.

Findings

Efficient recursive construction method for primitive polynomials.

Applicable to degrees of the form n2^k over finite fields.

Simplifies the generation process for cryptographic and coding applications.

Abstract

In this paper, a computationally simple and explicit method of constructing recursive sequence of primitive polynomials of degree $n2^k (k = 1, 2, 3,\ldots)$ over $\mathbb{F}_{q}$ is given.