The n-dimensional key equation and a decoding application
The author introduce the n-dimensional key equation, which exhibits the error-locator polynomial of an n-dimensional cyclic code as a product of n univariate polynomials and the error-evaluator polynomial as an n-variable polynomial. They then reinterpret these polynomials in the context of linear r...
Gespeichert in:
| Veröffentlicht in: | IEEE transactions on information theory 1994-01, Vol.40 (1), p.200-203 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 203 |
|---|---|
| container_issue | 1 |
| container_start_page | 200 |
| container_title | IEEE transactions on information theory |
| container_volume | 40 |
| creator | Chabanne, H. Norton, G.H. |
| description | The author introduce the n-dimensional key equation, which exhibits the error-locator polynomial of an n-dimensional cyclic code as a product of n univariate polynomials and the error-evaluator polynomial as an n-variable polynomial. They then reinterpret these polynomials in the context of linear recurring sequences. In particular, they reduce the decoding problem to successive application of the Berlekamp-Massey algorithm. With this new method, they are able to decode (up to half their minimum distance) many codes in a table of 2-D cyclic codes due to Jensen (1985).< > |
| doi_str_mv | 10.1109/18.272482 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_RIE</sourceid><recordid>TN_cdi_crossref_primary_10_1109_18_272482</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ieee_id>272482</ieee_id><sourcerecordid>28681619</sourcerecordid><originalsourceid>FETCH-LOGICAL-c306t-97ff43726ca1584a945dbfdc25c9b8a116e2d7689ba9e2278687799a35aad4af3</originalsourceid><addsrcrecordid>eNo9kDtPwzAUhS0EEqUwsDJ5QEgMKbbj54gQL6kSS5mjW_saDGmSxu3Qf09Kqk5XR-c733AJueZsxjlzD9zOhBHSihMy4UqZwmklT8mEMW4LJ6U9Jxc5_wxRKi4mxC2-kTZFSCtscmobqOkv7iiut7AZIoUmUKABfRtS80Wh6-rk_6tLchahznh1uFPy-fK8eHor5h-v70-P88KXTG8KZ2KUpRHaA1dWgpMqLGPwQnm3tMC5RhGMtm4JDoUwVltjnINSAQQJsZySu9Hb9e16i3lTrVL2WNfQYLvNlRgWXHM3gPcj6Ps25x5j1fVpBf2u4qzaP6fithqfM7C3BylkD3XsofEpHweSlUqLvfJmxBIiHtuD4w_72Wqt</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>28681619</pqid></control><display><type>article</type><title>The n-dimensional key equation and a decoding application</title><source>IEEE Electronic Library (IEL)</source><creator>Chabanne, H. ; Norton, G.H.</creator><creatorcontrib>Chabanne, H. ; Norton, G.H.</creatorcontrib><description>The author introduce the n-dimensional key equation, which exhibits the error-locator polynomial of an n-dimensional cyclic code as a product of n univariate polynomials and the error-evaluator polynomial as an n-variable polynomial. They then reinterpret these polynomials in the context of linear recurring sequences. In particular, they reduce the decoding problem to successive application of the Berlekamp-Massey algorithm. With this new method, they are able to decode (up to half their minimum distance) many codes in a table of 2-D cyclic codes due to Jensen (1985).< ></description><identifier>ISSN: 0018-9448</identifier><identifier>EISSN: 1557-9654</identifier><identifier>DOI: 10.1109/18.272482</identifier><identifier>CODEN: IETTAW</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Algebra ; Applied sciences ; Character generation ; Coding, codes ; Decoding ; Equations ; Error correction codes ; Exact sciences and technology ; Galois fields ; Information theory ; Information, signal and communications theory ; Polynomials ; Signal and communications theory ; Telecommunications and information theory</subject><ispartof>IEEE transactions on information theory, 1994-01, Vol.40 (1), p.200-203</ispartof><rights>1994 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c306t-97ff43726ca1584a945dbfdc25c9b8a116e2d7689ba9e2278687799a35aad4af3</citedby><cites>FETCH-LOGICAL-c306t-97ff43726ca1584a945dbfdc25c9b8a116e2d7689ba9e2278687799a35aad4af3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/272482$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,777,781,793,4010,27904,27905,27906,54739</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/272482$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=4035629$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Chabanne, H.</creatorcontrib><creatorcontrib>Norton, G.H.</creatorcontrib><title>The n-dimensional key equation and a decoding application</title><title>IEEE transactions on information theory</title><addtitle>TIT</addtitle><description>The author introduce the n-dimensional key equation, which exhibits the error-locator polynomial of an n-dimensional cyclic code as a product of n univariate polynomials and the error-evaluator polynomial as an n-variable polynomial. They then reinterpret these polynomials in the context of linear recurring sequences. In particular, they reduce the decoding problem to successive application of the Berlekamp-Massey algorithm. With this new method, they are able to decode (up to half their minimum distance) many codes in a table of 2-D cyclic codes due to Jensen (1985).< ></description><subject>Algebra</subject><subject>Applied sciences</subject><subject>Character generation</subject><subject>Coding, codes</subject><subject>Decoding</subject><subject>Equations</subject><subject>Error correction codes</subject><subject>Exact sciences and technology</subject><subject>Galois fields</subject><subject>Information theory</subject><subject>Information, signal and communications theory</subject><subject>Polynomials</subject><subject>Signal and communications theory</subject><subject>Telecommunications and information theory</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1994</creationdate><recordtype>article</recordtype><recordid>eNo9kDtPwzAUhS0EEqUwsDJ5QEgMKbbj54gQL6kSS5mjW_saDGmSxu3Qf09Kqk5XR-c733AJueZsxjlzD9zOhBHSihMy4UqZwmklT8mEMW4LJ6U9Jxc5_wxRKi4mxC2-kTZFSCtscmobqOkv7iiut7AZIoUmUKABfRtS80Wh6-rk_6tLchahznh1uFPy-fK8eHor5h-v70-P88KXTG8KZ2KUpRHaA1dWgpMqLGPwQnm3tMC5RhGMtm4JDoUwVltjnINSAQQJsZySu9Hb9e16i3lTrVL2WNfQYLvNlRgWXHM3gPcj6Ps25x5j1fVpBf2u4qzaP6fithqfM7C3BylkD3XsofEpHweSlUqLvfJmxBIiHtuD4w_72Wqt</recordid><startdate>199401</startdate><enddate>199401</enddate><creator>Chabanne, H.</creator><creator>Norton, G.H.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>199401</creationdate><title>The n-dimensional key equation and a decoding application</title><author>Chabanne, H. ; Norton, G.H.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c306t-97ff43726ca1584a945dbfdc25c9b8a116e2d7689ba9e2278687799a35aad4af3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1994</creationdate><topic>Algebra</topic><topic>Applied sciences</topic><topic>Character generation</topic><topic>Coding, codes</topic><topic>Decoding</topic><topic>Equations</topic><topic>Error correction codes</topic><topic>Exact sciences and technology</topic><topic>Galois fields</topic><topic>Information theory</topic><topic>Information, signal and communications theory</topic><topic>Polynomials</topic><topic>Signal and communications theory</topic><topic>Telecommunications and information theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chabanne, H.</creatorcontrib><creatorcontrib>Norton, G.H.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>IEEE transactions on information theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Chabanne, H.</au><au>Norton, G.H.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The n-dimensional key equation and a decoding application</atitle><jtitle>IEEE transactions on information theory</jtitle><stitle>TIT</stitle><date>1994-01</date><risdate>1994</risdate><volume>40</volume><issue>1</issue><spage>200</spage><epage>203</epage><pages>200-203</pages><issn>0018-9448</issn><eissn>1557-9654</eissn><coden>IETTAW</coden><abstract>The author introduce the n-dimensional key equation, which exhibits the error-locator polynomial of an n-dimensional cyclic code as a product of n univariate polynomials and the error-evaluator polynomial as an n-variable polynomial. They then reinterpret these polynomials in the context of linear recurring sequences. In particular, they reduce the decoding problem to successive application of the Berlekamp-Massey algorithm. With this new method, they are able to decode (up to half their minimum distance) many codes in a table of 2-D cyclic codes due to Jensen (1985).< ></abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/18.272482</doi><tpages>4</tpages></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | ISSN: 0018-9448 |
| ispartof | IEEE transactions on information theory, 1994-01, Vol.40 (1), p.200-203 |
| issn | 0018-9448 1557-9654 |
| language | eng |
| recordid | cdi_crossref_primary_10_1109_18_272482 |
| source | IEEE Electronic Library (IEL) |
| subjects | Algebra Applied sciences Character generation Coding, codes Decoding Equations Error correction codes Exact sciences and technology Galois fields Information theory Information, signal and communications theory Polynomials Signal and communications theory Telecommunications and information theory |
| title | The n-dimensional key equation and a decoding application |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-18T10%3A31%3A16IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_RIE&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20n-dimensional%20key%20equation%20and%20a%20decoding%20application&rft.jtitle=IEEE%20transactions%20on%20information%20theory&rft.au=Chabanne,%20H.&rft.date=1994-01&rft.volume=40&rft.issue=1&rft.spage=200&rft.epage=203&rft.pages=200-203&rft.issn=0018-9448&rft.eissn=1557-9654&rft.coden=IETTAW&rft_id=info:doi/10.1109/18.272482&rft_dat=%3Cproquest_RIE%3E28681619%3C/proquest_RIE%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=28681619&rft_id=info:pmid/&rft_ieee_id=272482&rfr_iscdi=true |