Self-Conjugate-Reciprocal Polynomials over Finite Fields and Self-Conjugate-Reciprocal Transformation

Annual Meeting in Mathematics 2023

Abstract

An interesting class of polynomials over finite fields, namely self-conjugate-reciprocal polynomials, has been studied here. Some elementary properties on their roots and a way to find all self-conjugate-reciprocal irreducible monic polynomials of a given degree are provided. Moreover, in the last part, we define a map taking a polynomial over a finite field with some conditions to a self-conjugate-reciprocal polynomial. Certain properties of the polynomial obtained from this map are investigated.