Some Properties of Generalized Self-reciprocal Polynomials over Finite Fields

TL;DR

This paper explores properties of generalized self-reciprocal polynomials over finite fields, focusing on divisibility and the parity of irreducible factors, extending known results to a broader class of polynomials.

Contribution

It introduces and analyzes a-self reciprocal polynomials, generalizing existing results on self-reciprocal polynomials over finite fields.

Findings

Characterization of divisibility properties of a-self reciprocal polynomials

Parity determination of the number of irreducible factors

Extension of known results to polynomials over finite fields of odd characteristic

Abstract

Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to a-self reciprocal polynomials defined in [4]. We consider some properties of the divisibility of a-reciprocal polynomials and characterize the parity of the number of irreducible factors for a-self reciprocal polynomials over finite fields of odd characteristic.