On Exponential Sums, Nowton identities and Dickson Polynomials over Finite Fields

2010/01/25 by Xiwang Cao, Lei Hu, Cao, Xiwang +1
Computer Science · Mathematics · #11T23 #Cellular Automata and Applications #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT #msc:11T23

paper · pdf · doi:10.48550/arxiv.1001.4305

18 pages

arxiv created 2010/01/25 · openalex publication_date 2010/01/25 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathbbF_q be a finite field, \mathbbF_q^s be an extension of \mathbbF_q, let f(x)∈ \mathbbF_q[x] be a polynomial of degree n with gcd(n,q)=1. We present a recursive formula for evaluating the exponential sum ∑_c∈ \mathbbF_q^sχ^(s)(f(x)). Let a and b be two elements in \mathbbF_q with a≠ 0, u be a positive integer. We obtain an estimate for the exponential sum ∑_c∈ \mathbbF^*_q^sχ^(s)(ac^u+bc^-1), where χ^(s) is the lifting of an additive character χ of \mathbbF_q. Some properties of the sequences constructed from these exponential sums are provided also.

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