On Some Exponential Sums Related to the Coulter's Polynomial
Minglong Qi, Shengwu Xiong, Jingling Yuan, Wenbi Rao, Luo Zhong
TL;DR
This paper derives formulas for exponential sums over finite fields related to Coulter's polynomial, leveraging Coulter's theorems on Weil sums, with potential applications in constructing linear codes with few weights.
Contribution
It provides new explicit formulas for exponential sums associated with Coulter's polynomial, expanding understanding of their properties and applications.
Findings
Formulas for exponential sums related to Coulter's polynomial derived.
Potential application in constructing linear codes with few weights identified.
Abstract
In this paper, the formulas of some exponential sums over finite field, related to the Coulter's polynomial, are settled based on the Coulter's theorems on Weil sums, which may have potential application in the construction of linear codes with few weights.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Coding theory and cryptography · Advanced Algebra and Geometry