Sections of the Del Pezzo surfaces and generalized weights
type: Item
instance of: scholarly article
title: Sections of the Del Pezzo surfaces and generalized weights
zbMATH Open document ID: 0926.94027
published in: Problems of Information Transmission
publication date: 1999-12-05T00:00:00Z
review text: Let \(C\) be an \([n,k;q]\) code that is a linear code of length \(n\) and dimension \(k\) over \(GF(q)\). For any subcode \(D\) of \(C\), let \(\chi (D)\) be the support of \(D\), i.e. the set of positions where not all the codewords of \(D\) are zero. Further, let \(w_S\) \((D):=|\chi(D)|\) be the support weight of \(D\). For \(1\leq r\leq k\), the \(r\)-th generalized Hamming weight of \(C\) is defined by \(d_r=d_r(C)= \min \{w_S(D)\mid D\) is an \([n,r;q]\) subcode of \(C\}\). The sequence \((d_1,d_2, \dots, d_k)\) is the weight hierarchy of \(C\). In this paper the author analyzes sections of split Del Pezzo surfaces and computes the weight hierarchy for algebraic-geometric codes constructed from Del Pezzo surfaces.
reviewed by: Giorgio Faina
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 51E15
Mathematics Subject Classification ID: 94B27
zbMATH DE Number: 1253949
zbMATH Keywords: linear code
zbMATH Keywords: split Del Pezzo surfaces
zbMATH Keywords: weight hierarchy
zbMATH Keywords: algebraic-geometric codes
author: Michael I. Boguslavsky
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1253949