Low Complexity Tail-Biting Trellises of Self-dual codes of Length 24, 32 and 40 over GF(2) and Z4 of Large Minimum Distance
We show in this article how the multi-stage encoding scheme proposed in [3] may be used to construct the [24] by using an extended [8, 4, 4] Hamming base code. An extension of the construction of [3] over Z4 yields self-dual codes over Z4 with parameters (for the Lee metric over Z4) [24, 12, 12] and...
Gespeichert in:
| Hauptverfasser: | , , , , |
|---|---|
| Format: | Buchkapitel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 66 |
|---|---|
| container_issue | |
| container_start_page | 57 |
| container_title | |
| container_volume | 2227 |
| creator | Cadic, E. Carlach, J.C. Olocco, G. Otmani, A. Tillich, J.P. |
| description | We show in this article how the multi-stage encoding scheme proposed in [3] may be used to construct the [24] by using an extended [8, 4, 4] Hamming base code. An extension of the construction of [3] over Z4 yields self-dual codes over Z4 with parameters (for the Lee metric over Z4) [24, 12, 12] and [32, 16, 12] by using the [8, 4, 6] octacode. Moreover, there is a natural Tanner graph associated to the construction of [3], and it turns out that all our constructions have Tanner graphs that have a cyclic structure which gives tail-biting trellises of low complexity: 16-state tail-biting trellises for the [24, 12, 8], [32, 16, 8], [40, 20, 8] binary codes, and 256-state tail-biting trellises for the [24, 12, 12] and [32, 16, 12] codes over Z4. |
| doi_str_mv | 10.1007/3-540-45624-4_6 |
| format | Book Chapter |
| fullrecord | <record><control><sourceid>proquest_pasca</sourceid><recordid>TN_cdi_pascalfrancis_primary_14047366</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>EBC3072785_12_69</sourcerecordid><originalsourceid>FETCH-LOGICAL-p1816-64837a47602ddd34e9f19f7c7ffe0368bfa1ea33b736eb37fdf4736a00705723</originalsourceid><addsrcrecordid>eNpFkUFvEzEQhU2BiqjkzNWXSiBhsD1ee32EQAtSEAdy4mI5u-PU4Owu9gao-PO4SaXOZUZvvpmR3hDyQvA3gnPzFlijOFONlooppx-RpTUtVO0omTOyEFoIBqDs44eetEKIJ2TBgUtmjYJzsrBN2zS2FfwZWZbyg9cAKQDsgvxbj3_oatxPCf_G-ZZufEzsfZzjsKObjCnFgoWOgX7DFFh_8Il2Y3-S1jjs5hsq1WsKkvqhp4rT8Tdmen31Ur46Kt_VkfR5h_RLHOL-sKcfYpn90OFz8jT4VHB5ny_I5urjZvWJrb9ef169W7NJtEIzrVowXhnNZd_3oNAGYYPpTAjIQbfb4AV6gK0BjVswoQ-qlr56yBsj4YJcntZOvnQ-hVxvx-KmHPc-3zpRTau4rhw7caW2hh1mtx3Hn8UJ7u7-4cBVf93RfFf_UXl5vzePvw5YZod3Ax0Oc_apu_HTjLk44EaatnFCOm3hP0wVhAo</addsrcrecordid><sourcetype>Index Database</sourcetype><iscdi>true</iscdi><recordtype>book_chapter</recordtype><pqid>EBC3072785_12_69</pqid></control><display><type>book_chapter</type><title>Low Complexity Tail-Biting Trellises of Self-dual codes of Length 24, 32 and 40 over GF(2) and Z4 of Large Minimum Distance</title><source>Springer Books</source><creator>Cadic, E. ; Carlach, J.C. ; Olocco, G. ; Otmani, A. ; Tillich, J.P.</creator><contributor>Shparlinski, Igor E ; Boztas, Serdar ; Shparlinski, Igor E. ; Boztaş, Serdar</contributor><creatorcontrib>Cadic, E. ; Carlach, J.C. ; Olocco, G. ; Otmani, A. ; Tillich, J.P. ; Shparlinski, Igor E ; Boztas, Serdar ; Shparlinski, Igor E. ; Boztaş, Serdar</creatorcontrib><description>We show in this article how the multi-stage encoding scheme proposed in [3] may be used to construct the [24] by using an extended [8, 4, 4] Hamming base code. An extension of the construction of [3] over Z4 yields self-dual codes over Z4 with parameters (for the Lee metric over Z4) [24, 12, 12] and [32, 16, 12] by using the [8, 4, 6] octacode. Moreover, there is a natural Tanner graph associated to the construction of [3], and it turns out that all our constructions have Tanner graphs that have a cyclic structure which gives tail-biting trellises of low complexity: 16-state tail-biting trellises for the [24, 12, 8], [32, 16, 8], [40, 20, 8] binary codes, and 256-state tail-biting trellises for the [24, 12, 12] and [32, 16, 12] codes over Z4.</description><identifier>ISSN: 0302-9743</identifier><identifier>ISBN: 9783540429111</identifier><identifier>ISBN: 3540429115</identifier><identifier>EISSN: 1611-3349</identifier><identifier>EISBN: 9783540456247</identifier><identifier>EISBN: 3540456244</identifier><identifier>DOI: 10.1007/3-540-45624-4_6</identifier><identifier>OCLC: 958559810</identifier><identifier>LCCallNum: QA150-272</identifier><language>eng</language><publisher>Germany: Springer Berlin / Heidelberg</publisher><subject>Applied sciences ; codes over Z ; Coding, codes ; Exact sciences and technology ; Information, signal and communications theory ; self-dual codes ; Signal and communications theory ; tail-biting trellises ; Tanner graph ; Telecommunications and information theory</subject><ispartof>Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 2001, Vol.2227, p.57-66</ispartof><rights>Springer-Verlag Berlin Heidelberg 2001</rights><rights>2002 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><relation>Lecture Notes in Computer Science</relation></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttps://ebookcentral.proquest.com/covers/3072785-l.jpg</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/3-540-45624-4_6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/3-540-45624-4_6$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>309,310,779,780,784,789,790,793,4049,4050,27924,38254,41441,42510</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=14047366$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><contributor>Shparlinski, Igor E</contributor><contributor>Boztas, Serdar</contributor><contributor>Shparlinski, Igor E.</contributor><contributor>Boztaş, Serdar</contributor><creatorcontrib>Cadic, E.</creatorcontrib><creatorcontrib>Carlach, J.C.</creatorcontrib><creatorcontrib>Olocco, G.</creatorcontrib><creatorcontrib>Otmani, A.</creatorcontrib><creatorcontrib>Tillich, J.P.</creatorcontrib><title>Low Complexity Tail-Biting Trellises of Self-dual codes of Length 24, 32 and 40 over GF(2) and Z4 of Large Minimum Distance</title><title>Applied Algebra, Algebraic Algorithms and Error-Correcting Codes</title><description>We show in this article how the multi-stage encoding scheme proposed in [3] may be used to construct the [24] by using an extended [8, 4, 4] Hamming base code. An extension of the construction of [3] over Z4 yields self-dual codes over Z4 with parameters (for the Lee metric over Z4) [24, 12, 12] and [32, 16, 12] by using the [8, 4, 6] octacode. Moreover, there is a natural Tanner graph associated to the construction of [3], and it turns out that all our constructions have Tanner graphs that have a cyclic structure which gives tail-biting trellises of low complexity: 16-state tail-biting trellises for the [24, 12, 8], [32, 16, 8], [40, 20, 8] binary codes, and 256-state tail-biting trellises for the [24, 12, 12] and [32, 16, 12] codes over Z4.</description><subject>Applied sciences</subject><subject>codes over Z</subject><subject>Coding, codes</subject><subject>Exact sciences and technology</subject><subject>Information, signal and communications theory</subject><subject>self-dual codes</subject><subject>Signal and communications theory</subject><subject>tail-biting trellises</subject><subject>Tanner graph</subject><subject>Telecommunications and information theory</subject><issn>0302-9743</issn><issn>1611-3349</issn><isbn>9783540429111</isbn><isbn>3540429115</isbn><isbn>9783540456247</isbn><isbn>3540456244</isbn><fulltext>true</fulltext><rsrctype>book_chapter</rsrctype><creationdate>2001</creationdate><recordtype>book_chapter</recordtype><recordid>eNpFkUFvEzEQhU2BiqjkzNWXSiBhsD1ee32EQAtSEAdy4mI5u-PU4Owu9gao-PO4SaXOZUZvvpmR3hDyQvA3gnPzFlijOFONlooppx-RpTUtVO0omTOyEFoIBqDs44eetEKIJ2TBgUtmjYJzsrBN2zS2FfwZWZbyg9cAKQDsgvxbj3_oatxPCf_G-ZZufEzsfZzjsKObjCnFgoWOgX7DFFh_8Il2Y3-S1jjs5hsq1WsKkvqhp4rT8Tdmen31Ur46Kt_VkfR5h_RLHOL-sKcfYpn90OFz8jT4VHB5ny_I5urjZvWJrb9ef169W7NJtEIzrVowXhnNZd_3oNAGYYPpTAjIQbfb4AV6gK0BjVswoQ-qlr56yBsj4YJcntZOvnQ-hVxvx-KmHPc-3zpRTau4rhw7caW2hh1mtx3Hn8UJ7u7-4cBVf93RfFf_UXl5vzePvw5YZod3Ax0Oc_apu_HTjLk44EaatnFCOm3hP0wVhAo</recordid><startdate>2001</startdate><enddate>2001</enddate><creator>Cadic, E.</creator><creator>Carlach, J.C.</creator><creator>Olocco, G.</creator><creator>Otmani, A.</creator><creator>Tillich, J.P.</creator><general>Springer Berlin / Heidelberg</general><general>Springer Berlin Heidelberg</general><general>Springer</general><scope>FFUUA</scope><scope>IQODW</scope></search><sort><creationdate>2001</creationdate><title>Low Complexity Tail-Biting Trellises of Self-dual codes of Length 24, 32 and 40 over GF(2) and Z4 of Large Minimum Distance</title><author>Cadic, E. ; Carlach, J.C. ; Olocco, G. ; Otmani, A. ; Tillich, J.P.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p1816-64837a47602ddd34e9f19f7c7ffe0368bfa1ea33b736eb37fdf4736a00705723</frbrgroupid><rsrctype>book_chapters</rsrctype><prefilter>book_chapters</prefilter><language>eng</language><creationdate>2001</creationdate><topic>Applied sciences</topic><topic>codes over Z</topic><topic>Coding, codes</topic><topic>Exact sciences and technology</topic><topic>Information, signal and communications theory</topic><topic>self-dual codes</topic><topic>Signal and communications theory</topic><topic>tail-biting trellises</topic><topic>Tanner graph</topic><topic>Telecommunications and information theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cadic, E.</creatorcontrib><creatorcontrib>Carlach, J.C.</creatorcontrib><creatorcontrib>Olocco, G.</creatorcontrib><creatorcontrib>Otmani, A.</creatorcontrib><creatorcontrib>Tillich, J.P.</creatorcontrib><collection>ProQuest Ebook Central - Book Chapters - Demo use only</collection><collection>Pascal-Francis</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Cadic, E.</au><au>Carlach, J.C.</au><au>Olocco, G.</au><au>Otmani, A.</au><au>Tillich, J.P.</au><au>Shparlinski, Igor E</au><au>Boztas, Serdar</au><au>Shparlinski, Igor E.</au><au>Boztaş, Serdar</au><format>book</format><genre>bookitem</genre><ristype>CHAP</ristype><atitle>Low Complexity Tail-Biting Trellises of Self-dual codes of Length 24, 32 and 40 over GF(2) and Z4 of Large Minimum Distance</atitle><btitle>Applied Algebra, Algebraic Algorithms and Error-Correcting Codes</btitle><seriestitle>Lecture Notes in Computer Science</seriestitle><date>2001</date><risdate>2001</risdate><volume>2227</volume><spage>57</spage><epage>66</epage><pages>57-66</pages><issn>0302-9743</issn><eissn>1611-3349</eissn><isbn>9783540429111</isbn><isbn>3540429115</isbn><eisbn>9783540456247</eisbn><eisbn>3540456244</eisbn><abstract>We show in this article how the multi-stage encoding scheme proposed in [3] may be used to construct the [24] by using an extended [8, 4, 4] Hamming base code. An extension of the construction of [3] over Z4 yields self-dual codes over Z4 with parameters (for the Lee metric over Z4) [24, 12, 12] and [32, 16, 12] by using the [8, 4, 6] octacode. Moreover, there is a natural Tanner graph associated to the construction of [3], and it turns out that all our constructions have Tanner graphs that have a cyclic structure which gives tail-biting trellises of low complexity: 16-state tail-biting trellises for the [24, 12, 8], [32, 16, 8], [40, 20, 8] binary codes, and 256-state tail-biting trellises for the [24, 12, 12] and [32, 16, 12] codes over Z4.</abstract><cop>Germany</cop><pub>Springer Berlin / Heidelberg</pub><doi>10.1007/3-540-45624-4_6</doi><oclcid>958559810</oclcid><tpages>10</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0302-9743 |
| ispartof | Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 2001, Vol.2227, p.57-66 |
| issn | 0302-9743 1611-3349 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_14047366 |
| source | Springer Books |
| subjects | Applied sciences codes over Z Coding, codes Exact sciences and technology Information, signal and communications theory self-dual codes Signal and communications theory tail-biting trellises Tanner graph Telecommunications and information theory |
| title | Low Complexity Tail-Biting Trellises of Self-dual codes of Length 24, 32 and 40 over GF(2) and Z4 of Large Minimum Distance |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-08T19%3A15%3A28IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_pasca&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=bookitem&rft.atitle=Low%20Complexity%20Tail-Biting%20Trellises%20of%20Self-dual%20codes%20of%20Length%2024,%2032%20and%2040%20over%20GF(2)%20and%20Z4%20of%20Large%20Minimum%20Distance&rft.btitle=Applied%20Algebra,%20Algebraic%20Algorithms%20and%20Error-Correcting%20Codes&rft.au=Cadic,%20E.&rft.date=2001&rft.volume=2227&rft.spage=57&rft.epage=66&rft.pages=57-66&rft.issn=0302-9743&rft.eissn=1611-3349&rft.isbn=9783540429111&rft.isbn_list=3540429115&rft_id=info:doi/10.1007/3-540-45624-4_6&rft_dat=%3Cproquest_pasca%3EEBC3072785_12_69%3C/proquest_pasca%3E%3Curl%3E%3C/url%3E&rft.eisbn=9783540456247&rft.eisbn_list=3540456244&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=EBC3072785_12_69&rft_id=info:pmid/&rfr_iscdi=true |