LDPC codes from triangle-free line sets
type: Item
instance of: scholarly article
title: LDPC codes from triangle-free line sets
zbMATH Open document ID: 1052.51008
DOI: 10.1023/B:DESI.0000029233.20866.41
author: Keith E. Mellinger
published in: Designs, Codes and Cryptography
publication date: 2004-08-16T00:00:00Z
review text: Let \(AG(n,q)\) and \(PG(n,q)\) be the finite affine and projective spaces respectively of dimension \(n\) over \(GF(q)\). A subset \(\mathcal L\) of lines of \(AG(n,q)\) or \(PG(n,q)\) is said to be triangle-free if no three nonconcurrent lines of \(\mathcal L\) form a triangle. If \(G\) is the bipartite graph whose vertices are the points of a finite space and whose edges are determined by natural inclusion, then the point-line graph associated with a triangle-free set turns out to have no cycles of length \(6\) and girth at least \(8\). It follows that the associated incidence matrix is relatively sparse and so can be used to construct a so-called low-density parity check code. In the paper under review the author gives two constructions of triangle-free sets and hence the parameters of the associated codes when \(q\) is sufficiently small.
Mathematics Subject Classification ID: 51E22
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 94B27
zbMATH DE Number: 2091526
zbMATH Keywords: cap
zbMATH Keywords: polarity
reviewed by: Antonio Cossidente
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: b:desi.0000029233.20866.41
OpenAlex ID: W2034782429
description: scientific article; zbMATH DE number 2091526