Linear block and convolutional MDS codes to required rate, distance and type
In: Arai, K. (eds) Intelligent Computing. SAI 2022, pp 129-157, Lecture Notes in Networks and Systems, vol 507. Springer, pp 129-157 (2022) Algebraic methods for the design of series of maximum distance separable (MDS) linear block and convolutional codes to required specifications and types are pre...
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| creator | Hurley, Ted |
| description | In: Arai, K. (eds) Intelligent Computing. SAI 2022, pp 129-157,
Lecture Notes in Networks and Systems, vol 507. Springer, pp 129-157 (2022) Algebraic methods for the design of series of maximum distance separable
(MDS) linear block and convolutional codes to required specifications and types
are presented. Algorithms are given to design codes to required rate and
required error-correcting capability and required types. Infinite series of
block codes with rate approaching a given rational $R$ with $0 |
| doi_str_mv | 10.48550/arxiv.2109.06721 |
| format | Article |
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Lecture Notes in Networks and Systems, vol 507. Springer, pp 129-157 (2022) Algebraic methods for the design of series of maximum distance separable
(MDS) linear block and convolutional codes to required specifications and types
are presented. Algorithms are given to design codes to required rate and
required error-correcting capability and required types. Infinite series of
block codes with rate approaching a given rational $R$ with $0<R<1$ and
relative distance over length approaching $(1-R)$ are designed. These can be
designed over fields of given characteristic $p$ or over fields of prime order
and can be specified to be of a particular type such as (i) dual-containing
under Euclidean inner product, (ii) dual-containing under Hermitian inner
product, (iii) quantum error-correcting, (iv) linear complementary dual (LCD).
Convolutional codes to required rate and distance and infinite series of
convolutional codes with rate approaching a given rational $R$ and distance
over length approaching $2(1-R)$ are designed. The designs are algebraic and
properties, including distances, are shown algebraically. Algebraic explicit
efficient decoding methods are referenced.</description><identifier>DOI: 10.48550/arxiv.2109.06721</identifier><language>eng</language><subject>Computer Science - Information Theory ; Mathematics - Information Theory</subject><creationdate>2021-09</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>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2109.06721$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.1007/978-3-031-10464-0_10$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.48550/arXiv.2109.06721$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Hurley, Ted</creatorcontrib><title>Linear block and convolutional MDS codes to required rate, distance and type</title><description>In: Arai, K. (eds) Intelligent Computing. SAI 2022, pp 129-157,
Lecture Notes in Networks and Systems, vol 507. Springer, pp 129-157 (2022) Algebraic methods for the design of series of maximum distance separable
(MDS) linear block and convolutional codes to required specifications and types
are presented. Algorithms are given to design codes to required rate and
required error-correcting capability and required types. Infinite series of
block codes with rate approaching a given rational $R$ with $0<R<1$ and
relative distance over length approaching $(1-R)$ are designed. These can be
designed over fields of given characteristic $p$ or over fields of prime order
and can be specified to be of a particular type such as (i) dual-containing
under Euclidean inner product, (ii) dual-containing under Hermitian inner
product, (iii) quantum error-correcting, (iv) linear complementary dual (LCD).
Convolutional codes to required rate and distance and infinite series of
convolutional codes with rate approaching a given rational $R$ and distance
over length approaching $2(1-R)$ are designed. The designs are algebraic and
properties, including distances, are shown algebraically. Algebraic explicit
efficient decoding methods are referenced.</description><subject>Computer Science - Information Theory</subject><subject>Mathematics - Information Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNpjYJA0NNAzsTA1NdBPLKrILNMzMjSw1DMwMzcy5GTw8cnMS00sUkjKyU_OVkjMS1FIzs8ry88pLcnMz0vMUfB1CQaKpKQWK5TkKxSlFpZmFqWmKBQllqTqKKRkFpck5iWngrWVVBak8jCwpiXmFKfyQmluBnk31xBnD12wvfEFRZm5iUWV8SD748H2GxNWAQC8TDqo</recordid><startdate>20210914</startdate><enddate>20210914</enddate><creator>Hurley, Ted</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20210914</creationdate><title>Linear block and convolutional MDS codes to required rate, distance and type</title><author>Hurley, Ted</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_2109_067213</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Computer Science - Information Theory</topic><topic>Mathematics - Information Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Hurley, Ted</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>Hurley, Ted</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Linear block and convolutional MDS codes to required rate, distance and type</atitle><date>2021-09-14</date><risdate>2021</risdate><abstract>In: Arai, K. (eds) Intelligent Computing. SAI 2022, pp 129-157,
Lecture Notes in Networks and Systems, vol 507. Springer, pp 129-157 (2022) Algebraic methods for the design of series of maximum distance separable
(MDS) linear block and convolutional codes to required specifications and types
are presented. Algorithms are given to design codes to required rate and
required error-correcting capability and required types. Infinite series of
block codes with rate approaching a given rational $R$ with $0<R<1$ and
relative distance over length approaching $(1-R)$ are designed. These can be
designed over fields of given characteristic $p$ or over fields of prime order
and can be specified to be of a particular type such as (i) dual-containing
under Euclidean inner product, (ii) dual-containing under Hermitian inner
product, (iii) quantum error-correcting, (iv) linear complementary dual (LCD).
Convolutional codes to required rate and distance and infinite series of
convolutional codes with rate approaching a given rational $R$ and distance
over length approaching $2(1-R)$ are designed. The designs are algebraic and
properties, including distances, are shown algebraically. Algebraic explicit
efficient decoding methods are referenced.</abstract><doi>10.48550/arxiv.2109.06721</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Information Theory Mathematics - Information Theory |
| title | Linear block and convolutional MDS codes to required rate, distance and type |
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