Divisibility properties and new bounds for cyclic codes and exponential sums in one and several variables
type: Item
instance of: scholarly article
title: Divisibility properties and new bounds for cyclic codes and exponential sums in one and several variables
zbMATH Open document ID: 0809.11080
DOI: 10.1007/BF01438279
published in: Applicable Algebra in Engineering, Communication and Computing
publication date: 1994-04-24T00:00:00Z
review text: Using Serre's sharp estimates for the number of rational points on an algebraic curve over a finite field and divisibility properties for exponential sums the authors derive new bounds for exponential sums in one and several variables. This leads to an improvement of previous bounds for the minimum distance of the duals of BCH codes. Moreover the divisibility properties imply the existence of gaps in the weight distribution of certain cyclic codes.
Mathematics Subject Classification ID: 11T71
Mathematics Subject Classification ID: 11T23
Mathematics Subject Classification ID: 94B15
Mathematics Subject Classification ID: 94B65
zbMATH DE Number: 556285
zbMATH Keywords: divisibility
zbMATH Keywords: bounds for exponential sums
zbMATH Keywords: minimum distance
zbMATH Keywords: duals of BCH codes
zbMATH Keywords: cyclic codes
author: Simon Litsyn
author: Carlos Julio Moreno
author: Oscar Moreno
reviewed by: Gabriele Steidl
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01438279
OpenAlex ID: W1973236070
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description: scientific article; zbMATH DE number 556285