A \(p\)-adic Serre bound
type: Item
instance of: scholarly article
title: A \(p\)-adic Serre bound
zbMATH Open document ID: 0921.11064
author: Oscar Moreno
author: Carlos Julio Moreno
published in: Finite Fields and their Applications
publication date: 1999-09-29T00:00:00Z
review text: The main result of this paper combines a technique due to Serre with the authors own improvement of results due to Ax and Katz to produce a general \(p\)-adic Serre bound. This improves and generalizes earlier results by the same authors. The work in the paper was motivated by coding theory and has immediate applications that give minimum distance estimates for cyclic codes. Motivated by algebraic geometric Goppa codes the authors estimate the number of rational points of complete intersections. The authors give a \(p\)-adic Serre bound for complete intersections and estimate the Betti number for a complete intersection.
reviewed by: Tor Helleseth
Mathematics Subject Classification ID: 11T23
Mathematics Subject Classification ID: 94B27
Mathematics Subject Classification ID: 11T71
Mathematics Subject Classification ID: 94B15
Mathematics Subject Classification ID: 14G05
Mathematics Subject Classification ID: 14G20
zbMATH DE Number: 1236196
zbMATH Keywords: \(p\)-adic Serre bound
zbMATH Keywords: minimum distance estimates for cyclic codes
zbMATH Keywords: algebraic geometric Goppa codes
zbMATH Keywords: number of rational points of complete intersections
zbMATH Keywords: Betti number
MaRDI profile type: Publication
full work available at URL: ffta.1997.0193
OpenAlex ID: W1988664319
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DOI: 10.1006/FFTA.1997.0193
description: scientific article; zbMATH DE number 1236196