Quantum MDS and synchronizable codes from cyclic codes of length 5ps over Fpm
For any odd prime p ≠ 5 , the structures of cyclic codes of length 5 p s over F p m are applied to construct quantum error-correcting codes (briefly, QEC codes). Some new QEC codes are provided in the sense that their parameters are different from all the previous constructions. We give all quantum...
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| Veröffentlicht in: | Applicable algebra in engineering, communication and computing communication and computing, 2023, Vol.34 (6), p.931-964 |
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| container_title | Applicable algebra in engineering, communication and computing |
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| creator | Dinh, Hai Q. Nguyen, Bac T. Tansuchat, Roengchai |
| description | For any odd prime
p
≠
5
, the structures of cyclic codes of length
5
p
s
over
F
p
m
are applied to construct quantum error-correcting codes (briefly, QEC codes). Some new QEC codes are provided in the sense that their parameters are different from all the previous constructions. We give all quantum maximum-distance-separable (briefly, qMDS codes) constructed by the CSS construction. We also construct quantum synchronizable codes (briefly, QSCs). To enrich the variety of available QSCs, many new QSCs are constructed to illustrate our results. Among them, there are QSCs codes with shorter lengths and much larger minimum distances than known primitive narrow-sense BCH codes. |
| doi_str_mv | 10.1007/s00200-021-00531-6 |
| format | Article |
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p
≠
5
, the structures of cyclic codes of length
5
p
s
over
F
p
m
are applied to construct quantum error-correcting codes (briefly, QEC codes). Some new QEC codes are provided in the sense that their parameters are different from all the previous constructions. We give all quantum maximum-distance-separable (briefly, qMDS codes) constructed by the CSS construction. We also construct quantum synchronizable codes (briefly, QSCs). To enrich the variety of available QSCs, many new QSCs are constructed to illustrate our results. Among them, there are QSCs codes with shorter lengths and much larger minimum distances than known primitive narrow-sense BCH codes.</description><identifier>ISSN: 0938-1279</identifier><identifier>EISSN: 1432-0622</identifier><identifier>DOI: 10.1007/s00200-021-00531-6</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Artificial Intelligence ; BCH codes ; Computer Hardware ; Computer Science ; Error correcting codes ; Error correction ; Original Paper ; Symbolic and Algebraic Manipulation ; Theory of Computation</subject><ispartof>Applicable algebra in engineering, communication and computing, 2023, Vol.34 (6), p.931-964</ispartof><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021</rights><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-p157t-42c3979ccaa203b7a89e7308376460ba235672a7591f6cbe1e0a6991a8a8b9943</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00200-021-00531-6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00200-021-00531-6$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Dinh, Hai Q.</creatorcontrib><creatorcontrib>Nguyen, Bac T.</creatorcontrib><creatorcontrib>Tansuchat, Roengchai</creatorcontrib><title>Quantum MDS and synchronizable codes from cyclic codes of length 5ps over Fpm</title><title>Applicable algebra in engineering, communication and computing</title><addtitle>AAECC</addtitle><description>For any odd prime
p
≠
5
, the structures of cyclic codes of length
5
p
s
over
F
p
m
are applied to construct quantum error-correcting codes (briefly, QEC codes). Some new QEC codes are provided in the sense that their parameters are different from all the previous constructions. We give all quantum maximum-distance-separable (briefly, qMDS codes) constructed by the CSS construction. We also construct quantum synchronizable codes (briefly, QSCs). To enrich the variety of available QSCs, many new QSCs are constructed to illustrate our results. Among them, there are QSCs codes with shorter lengths and much larger minimum distances than known primitive narrow-sense BCH codes.</description><subject>Artificial Intelligence</subject><subject>BCH codes</subject><subject>Computer Hardware</subject><subject>Computer Science</subject><subject>Error correcting codes</subject><subject>Error correction</subject><subject>Original Paper</subject><subject>Symbolic and Algebraic Manipulation</subject><subject>Theory of Computation</subject><issn>0938-1279</issn><issn>1432-0622</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNpFkEtLAzEUhYMoWKt_wFXAdfQmmbyWUm0VWkTUdcikmT6YZsZkRqi_3tEWXF3O5eMc-BC6pnBLAdRdBmAABBglAIJTIk_QiBacEZCMnaIRGK4JZcqco4uctwAgTaFGaPHau9j1O7x4eMMuLnHeR79OTdx8u7IO2DfLkHGVmh32e19v_PHTVLgOcdWtsWiH9BUSnra7S3RWuTqHq-Mdo4_p4_vkicxfZs-T-zlpqVAdKZjnRhnvnWPAS-W0CYqD5koWEkrHuJCKOSUMraQvAw3gpDHUaadLYwo-RjeH3jY1n33Ind02fYrDpGVaiUJoQ9VA8QOV27SJq5D-KQr215s9eLODN_vnzUr-A6qMXrI</recordid><startdate>2023</startdate><enddate>2023</enddate><creator>Dinh, Hai Q.</creator><creator>Nguyen, Bac T.</creator><creator>Tansuchat, Roengchai</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope/></search><sort><creationdate>2023</creationdate><title>Quantum MDS and synchronizable codes from cyclic codes of length 5ps over Fpm</title><author>Dinh, Hai Q. ; Nguyen, Bac T. ; Tansuchat, Roengchai</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p157t-42c3979ccaa203b7a89e7308376460ba235672a7591f6cbe1e0a6991a8a8b9943</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Artificial Intelligence</topic><topic>BCH codes</topic><topic>Computer Hardware</topic><topic>Computer Science</topic><topic>Error correcting codes</topic><topic>Error correction</topic><topic>Original Paper</topic><topic>Symbolic and Algebraic Manipulation</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dinh, Hai Q.</creatorcontrib><creatorcontrib>Nguyen, Bac T.</creatorcontrib><creatorcontrib>Tansuchat, Roengchai</creatorcontrib><jtitle>Applicable algebra in engineering, communication and computing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dinh, Hai Q.</au><au>Nguyen, Bac T.</au><au>Tansuchat, Roengchai</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Quantum MDS and synchronizable codes from cyclic codes of length 5ps over Fpm</atitle><jtitle>Applicable algebra in engineering, communication and computing</jtitle><stitle>AAECC</stitle><date>2023</date><risdate>2023</risdate><volume>34</volume><issue>6</issue><spage>931</spage><epage>964</epage><pages>931-964</pages><issn>0938-1279</issn><eissn>1432-0622</eissn><abstract>For any odd prime
p
≠
5
, the structures of cyclic codes of length
5
p
s
over
F
p
m
are applied to construct quantum error-correcting codes (briefly, QEC codes). Some new QEC codes are provided in the sense that their parameters are different from all the previous constructions. We give all quantum maximum-distance-separable (briefly, qMDS codes) constructed by the CSS construction. We also construct quantum synchronizable codes (briefly, QSCs). To enrich the variety of available QSCs, many new QSCs are constructed to illustrate our results. Among them, there are QSCs codes with shorter lengths and much larger minimum distances than known primitive narrow-sense BCH codes.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00200-021-00531-6</doi><tpages>34</tpages></addata></record> |
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| identifier | ISSN: 0938-1279 |
| ispartof | Applicable algebra in engineering, communication and computing, 2023, Vol.34 (6), p.931-964 |
| issn | 0938-1279 1432-0622 |
| language | eng |
| recordid | cdi_proquest_journals_2875458917 |
| source | SpringerLink Journals |
| subjects | Artificial Intelligence BCH codes Computer Hardware Computer Science Error correcting codes Error correction Original Paper Symbolic and Algebraic Manipulation Theory of Computation |
| title | Quantum MDS and synchronizable codes from cyclic codes of length 5ps over Fpm |
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