Third Power of the Reversed Dickson Polynomial over Finite Fields

2011/04/01 by Xiang‐dong Hou, Xiang-dong Hou, Hou, Xiang-dong
Computer Science · Mathematics · #11T06 #Coding theory and cryptography #Combinatorics (math.CO) #Digital Filter Design and Implementation #FOS: Mathematics #Polynomial and algebraic computation #math.CO #msc:11T06

paper · pdf · doi:10.48550/arxiv.1104.0201

17 pages

arxiv created 2011/04/01 · openalex publication_date 2011/04/01 · arxiv updated 2011/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let D_n(1,x) be the nth reversed Dickson polynomial. The power sums ∑_{a∈\Bbb Fq}D_n(1,a)ⁱ, i=1,2, have been determined recently. In this paper we give an evaluation of the sum ∑_{a∈\Bbb Fq}D_n(1,a)³. This result implies new necessary conditions for D_n(1,x) to be a permutation polynomial over \Bbb F_q.

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