Parity-check Codes from Disjunct Matrices

The matrix representations of linear codes have been well-studied for use as disjunct matrices. However, no connection has previously been made between the properties of disjunct matrices and the parity-check codes obtained from them. This paper makes this connection for the first time. We provide s...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2024-07
Hauptverfasser: Haymaker, Kathryn, McMillon, Emily
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Haymaker, Kathryn
McMillon, Emily
description The matrix representations of linear codes have been well-studied for use as disjunct matrices. However, no connection has previously been made between the properties of disjunct matrices and the parity-check codes obtained from them. This paper makes this connection for the first time. We provide some fundamental results on parity-check codes from general disjunct matrices (in particular, a minimum distance bound). We then consider three specific constructions of disjunct matrices and provide parameters of their corresponding parity-check codes including rate, distance, girth, and density. We show that, by choosing the correct parameters, the codes we construct have the best possible error-correction performance after one round of bit-flipping decoding with regard to a modified version of Gallager's bit-flipping decoding algorithm.
format Article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2913560499</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2913560499</sourcerecordid><originalsourceid>FETCH-proquest_journals_29135604993</originalsourceid><addsrcrecordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mTQDEgsyiyp1E3OSE3OVnDOT0ktVkgrys9VcMkszirNSy5R8E0sKcpMTi3mYWBNS8wpTuWF0twMym6uIc4eugVF-YWlqcUl8Vn5pUV5QKl4I0tDY1MzAxNLS2PiVAEAwrEwUA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2913560499</pqid></control><display><type>article</type><title>Parity-check Codes from Disjunct Matrices</title><source>Freely Accessible Journals at publisher websites</source><creator>Haymaker, Kathryn ; McMillon, Emily</creator><creatorcontrib>Haymaker, Kathryn ; McMillon, Emily</creatorcontrib><description>The matrix representations of linear codes have been well-studied for use as disjunct matrices. However, no connection has previously been made between the properties of disjunct matrices and the parity-check codes obtained from them. This paper makes this connection for the first time. We provide some fundamental results on parity-check codes from general disjunct matrices (in particular, a minimum distance bound). We then consider three specific constructions of disjunct matrices and provide parameters of their corresponding parity-check codes including rate, distance, girth, and density. We show that, by choosing the correct parameters, the codes we construct have the best possible error-correction performance after one round of bit-flipping decoding with regard to a modified version of Gallager's bit-flipping decoding algorithm.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Algorithms ; Decoding ; Error correction ; Mathematical analysis ; Matrix representation ; Parameters ; Parity</subject><ispartof>arXiv.org, 2024-07</ispartof><rights>2024. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>781,785</link.rule.ids></links><search><creatorcontrib>Haymaker, Kathryn</creatorcontrib><creatorcontrib>McMillon, Emily</creatorcontrib><title>Parity-check Codes from Disjunct Matrices</title><title>arXiv.org</title><description>The matrix representations of linear codes have been well-studied for use as disjunct matrices. However, no connection has previously been made between the properties of disjunct matrices and the parity-check codes obtained from them. This paper makes this connection for the first time. We provide some fundamental results on parity-check codes from general disjunct matrices (in particular, a minimum distance bound). We then consider three specific constructions of disjunct matrices and provide parameters of their corresponding parity-check codes including rate, distance, girth, and density. We show that, by choosing the correct parameters, the codes we construct have the best possible error-correction performance after one round of bit-flipping decoding with regard to a modified version of Gallager's bit-flipping decoding algorithm.</description><subject>Algorithms</subject><subject>Decoding</subject><subject>Error correction</subject><subject>Mathematical analysis</subject><subject>Matrix representation</subject><subject>Parameters</subject><subject>Parity</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mTQDEgsyiyp1E3OSE3OVnDOT0ktVkgrys9VcMkszirNSy5R8E0sKcpMTi3mYWBNS8wpTuWF0twMym6uIc4eugVF-YWlqcUl8Vn5pUV5QKl4I0tDY1MzAxNLS2PiVAEAwrEwUA</recordid><startdate>20240729</startdate><enddate>20240729</enddate><creator>Haymaker, Kathryn</creator><creator>McMillon, Emily</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20240729</creationdate><title>Parity-check Codes from Disjunct Matrices</title><author>Haymaker, Kathryn ; McMillon, Emily</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_29135604993</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Algorithms</topic><topic>Decoding</topic><topic>Error correction</topic><topic>Mathematical analysis</topic><topic>Matrix representation</topic><topic>Parameters</topic><topic>Parity</topic><toplevel>online_resources</toplevel><creatorcontrib>Haymaker, Kathryn</creatorcontrib><creatorcontrib>McMillon, Emily</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Access via ProQuest (Open Access)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Haymaker, Kathryn</au><au>McMillon, Emily</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Parity-check Codes from Disjunct Matrices</atitle><jtitle>arXiv.org</jtitle><date>2024-07-29</date><risdate>2024</risdate><eissn>2331-8422</eissn><abstract>The matrix representations of linear codes have been well-studied for use as disjunct matrices. However, no connection has previously been made between the properties of disjunct matrices and the parity-check codes obtained from them. This paper makes this connection for the first time. We provide some fundamental results on parity-check codes from general disjunct matrices (in particular, a minimum distance bound). We then consider three specific constructions of disjunct matrices and provide parameters of their corresponding parity-check codes including rate, distance, girth, and density. We show that, by choosing the correct parameters, the codes we construct have the best possible error-correction performance after one round of bit-flipping decoding with regard to a modified version of Gallager's bit-flipping decoding algorithm.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2024-07
issn 2331-8422
language eng
recordid cdi_proquest_journals_2913560499
source Freely Accessible Journals at publisher websites
subjects Algorithms
Decoding
Error correction
Mathematical analysis
Matrix representation
Parameters
Parity
title Parity-check Codes from Disjunct Matrices
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-17T18%3A56%3A04IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Parity-check%20Codes%20from%20Disjunct%20Matrices&rft.jtitle=arXiv.org&rft.au=Haymaker,%20Kathryn&rft.date=2024-07-29&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2913560499%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2913560499&rft_id=info:pmid/&rfr_iscdi=true