Weight distributions of subfield subcodes of algebraic-geometrical codes
type: Item
instance of: scholarly article
title: Weight distributions of subfield subcodes of algebraic-geometrical codes
zbMATH Open document ID: 0732.94012
published in: Problems of Information Transmission
publication date: 1991-01-01T00:00:00Z
review text: In the paper some properties of subcodes of algebraic-geometric codes over prime subfields are investigated. In particular, the weighted distributions of these codes are discussed. Two theorems that describe differences between these distributions and those obtained for random codes, i.e., with binomial weight distributions, are given. It has been shown that for sufficiently long codes the weight distributions of algebraic-geometric codes become very close to appropriate weight distributions of random codes. To prove the theorems the authors use Stirling formulae and Weil-Bombieri estimations for exponential sums in finite fields. The paper brings some new, interesting results that extend earlier ones (e.g., Goppa's results) obtained in the area of algebraic- geometric codes.
Mathematics Subject Classification ID: 94B15
Mathematics Subject Classification ID: 94B27
Mathematics Subject Classification ID: 11T23
Mathematics Subject Classification ID: 11B73
zbMATH DE Number: 4211966
zbMATH Keywords: subcodes of algebraic-geometric codes over prime subfields
zbMATH Keywords: weighted distributions
zbMATH Keywords: Stirling formulae
zbMATH Keywords: Weil-Bombieri estimations for exponential sums in finite fields
author: Serge Vlăduţ
author: Alexei N. Skorobogatov
reviewed by: Józef Woźniak
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4211966