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...
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| 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. |
| doi_str_mv | 10.48550/arxiv.2311.17262 |
| format | Article |
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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>DOI: 10.48550/arxiv.2311.17262</identifier><language>eng</language><subject>Computer Science - Information Theory ; Mathematics - Information Theory</subject><creationdate>2023-11</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,781,886</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2311.17262$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2311.17262$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Haymaker, Kathryn</creatorcontrib><creatorcontrib>McMillon, Emily</creatorcontrib><title>Parity-check Codes from Disjunct Matrices</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>Computer Science - Information Theory</subject><subject>Mathematics - Information Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzrkOgkAUheFpLAz6AFbSWoCzADOWBtdEo4U9uQ73xnHPgEbf3ohWp_lz8jHWEzxOTJryIfiXe8ZSCRELLTPZZoMteFe_I3tAewrzW4lVSP52CSeuOj6utg7XUHtnseqwFsG5wu5_A7abTXf5Ilpt5st8vIog0zJCIwG1yLQSI8s5aq7QyoRSiwkqbQxlCYHRZLAplBwZ2AutaG9LolIFrP-7bazF3bsL-HfxNReNWX0A_I07WQ</recordid><startdate>20231128</startdate><enddate>20231128</enddate><creator>Haymaker, Kathryn</creator><creator>McMillon, Emily</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20231128</creationdate><title>Parity-check Codes from Disjunct Matrices</title><author>Haymaker, Kathryn ; McMillon, Emily</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a672-e82ae7167319c00e703ec24f5ce4e3788f64fa87f8e319c03298ab173fbcdffd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Computer Science - Information Theory</topic><topic>Mathematics - Information Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Haymaker, Kathryn</creatorcontrib><creatorcontrib>McMillon, Emily</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Haymaker, Kathryn</au><au>McMillon, Emily</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Parity-check Codes from Disjunct Matrices</atitle><date>2023-11-28</date><risdate>2023</risdate><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><doi>10.48550/arxiv.2311.17262</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Information Theory Mathematics - Information Theory |
| title | Parity-check Codes from Disjunct Matrices |
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