Palindromic Polynomials over Finite Fields

2022/10/27 by G. D. Price, Price, Geoffrey, Katherine Thompson +1
Computer Science · Mathematics · #11T06 #15A06 #Algebraic Geometry and Number Theory #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2210.15703

openalex publication_date 2022/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any finite field \mathbbF and any positive integer n we count the number of monic polynomials of degree n over \mathbbF with nonzero constant coefficient and a self-reciprocal factor of any specified degree. An application is given for systems of linear equations over \mathbbF of index 2.

Related

• Enumeration of self-reciprocal irreducible monic polynomials with prescribed leading coefficients over a finite field
• Improved error bounds for the number of irreducible polynomials and self-reciprocal irreducible monic polynomials with prescribed coefficients over a finite field
• Pairs of intertwined integer sequences
• On the enumeration of polynomials with prescribed factorization pattern
• Staircase palindromic polynomials