Unidirectional covering codes
A code C/spl sube/Z/sup n//sub 2/, where Z/sub 2/={0,1}, has unidirectional covering radius R if R is the smallest integer so that any word in Z/sup n//sub 2/ can be obtained from at least one codeword c/spl isin/C by replacing either 1s by 0s in at most R coordinates or 0s by 1s in at most R coordi...
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| Veröffentlicht in: | IEEE transactions on information theory 2006-01, Vol.52 (1), p.336-340 |
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| container_title | IEEE transactions on information theory |
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| creator | Ostergard, P.R.J. Seuranen, E.A. |
| description | A code C/spl sube/Z/sup n//sub 2/, where Z/sub 2/={0,1}, has unidirectional covering radius R if R is the smallest integer so that any word in Z/sup n//sub 2/ can be obtained from at least one codeword c/spl isin/C by replacing either 1s by 0s in at most R coordinates or 0s by 1s in at most R coordinates. The minimum cardinality of such a code is denoted by E(n,R). Upper bounds on this function are here obtained by constructing codes using tabu search; lower bounds, on the other hand, are mainly obtained by integer programming and exhaustive search. Best known bounds on E(n,R) for n/spl les/13 and R/spl les/6 are tabulated. |
| doi_str_mv | 10.1109/TIT.2005.860449 |
| format | Article |
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The minimum cardinality of such a code is denoted by E(n,R). Upper bounds on this function are here obtained by constructing codes using tabu search; lower bounds, on the other hand, are mainly obtained by integer programming and exhaustive search. Best known bounds on E(n,R) for n/spl les/13 and R/spl les/6 are tabulated.</description><identifier>ISSN: 0018-9448</identifier><identifier>EISSN: 1557-9654</identifier><identifier>DOI: 10.1109/TIT.2005.860449</identifier><identifier>CODEN: IETTAW</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Applied sciences ; Codes ; Coding, codes ; Construction ; Covering ; Covering codes ; Data compression ; Error correction codes ; Exact sciences and technology ; Information theory ; Information, signal and communications theory ; Integer programming ; Linear programming ; Lower bounds ; Mathematical models ; Searching ; Signal and communications theory ; Tabu search ; Telecommunications and information theory ; unidirectional codes ; Upper bound ; Upper bounds</subject><ispartof>IEEE transactions on information theory, 2006-01, Vol.52 (1), p.336-340</ispartof><rights>2006 INIST-CNRS</rights><rights>Copyright Institute of Electrical and Electronics Engineers, Inc. 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The minimum cardinality of such a code is denoted by E(n,R). Upper bounds on this function are here obtained by constructing codes using tabu search; lower bounds, on the other hand, are mainly obtained by integer programming and exhaustive search. Best known bounds on E(n,R) for n/spl les/13 and R/spl les/6 are tabulated.</description><subject>Applied sciences</subject><subject>Codes</subject><subject>Coding, codes</subject><subject>Construction</subject><subject>Covering</subject><subject>Covering codes</subject><subject>Data compression</subject><subject>Error correction codes</subject><subject>Exact sciences and technology</subject><subject>Information theory</subject><subject>Information, signal and communications theory</subject><subject>Integer programming</subject><subject>Linear programming</subject><subject>Lower bounds</subject><subject>Mathematical models</subject><subject>Searching</subject><subject>Signal and communications theory</subject><subject>Tabu search</subject><subject>Telecommunications and information theory</subject><subject>unidirectional codes</subject><subject>Upper bound</subject><subject>Upper bounds</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kE1LAzEQhoMoWKtnDyKIoHjZNtnNZJOjFD8KBS_tOWSzs5Ky3a1JK_jvndJCwYOnTJhnXmYexq4FHwnBzXg-nY9yzmGkFZfSnLCBACgzo0CesgHnQmdGSn3OLlJa0leCyAfsdtGFOkT0m9B3rr3z_TfG0H1SUWO6ZGeNaxNeHd4hW7y-zCfv2ezjbTp5nmW-0PkmMyY30oBTHKuqBEMLOIFc-1whB6WgEaYowYNvaqGN9tpp4aGuCsMbrLAYssd97jr2X1tMG7sKyWPbug77bbK55iCMAAKf_gVFoYDO5nlJ6P0fdNlvI91IlAEKE1oTNN5DPvYpRWzsOoaViz9WcLvTakmr3Wm1e6008XCIdcm7tomu8yEdx8qi1BRN3M2eC4h4bIOSJL74BbAofTE</recordid><startdate>200601</startdate><enddate>200601</enddate><creator>Ostergard, P.R.J.</creator><creator>Seuranen, E.A.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>F28</scope><scope>FR3</scope></search><sort><creationdate>200601</creationdate><title>Unidirectional covering codes</title><author>Ostergard, P.R.J. ; Seuranen, E.A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c382t-9929495a60ebb759604a1e08c26e05665f19375c5cfd1898c8a81c5db390febe3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Applied sciences</topic><topic>Codes</topic><topic>Coding, codes</topic><topic>Construction</topic><topic>Covering</topic><topic>Covering codes</topic><topic>Data compression</topic><topic>Error correction codes</topic><topic>Exact sciences and technology</topic><topic>Information theory</topic><topic>Information, signal and communications theory</topic><topic>Integer programming</topic><topic>Linear programming</topic><topic>Lower bounds</topic><topic>Mathematical models</topic><topic>Searching</topic><topic>Signal and communications theory</topic><topic>Tabu search</topic><topic>Telecommunications and information theory</topic><topic>unidirectional codes</topic><topic>Upper bound</topic><topic>Upper bounds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ostergard, P.R.J.</creatorcontrib><creatorcontrib>Seuranen, E.A.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications 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><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><jtitle>IEEE transactions on information theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Ostergard, P.R.J.</au><au>Seuranen, E.A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Unidirectional covering codes</atitle><jtitle>IEEE transactions on information theory</jtitle><stitle>TIT</stitle><date>2006-01</date><risdate>2006</risdate><volume>52</volume><issue>1</issue><spage>336</spage><epage>340</epage><pages>336-340</pages><issn>0018-9448</issn><eissn>1557-9654</eissn><coden>IETTAW</coden><abstract>A code C/spl sube/Z/sup n//sub 2/, where Z/sub 2/={0,1}, has unidirectional covering radius R if R is the smallest integer so that any word in Z/sup n//sub 2/ can be obtained from at least one codeword c/spl isin/C by replacing either 1s by 0s in at most R coordinates or 0s by 1s in at most R coordinates. The minimum cardinality of such a code is denoted by E(n,R). Upper bounds on this function are here obtained by constructing codes using tabu search; lower bounds, on the other hand, are mainly obtained by integer programming and exhaustive search. Best known bounds on E(n,R) for n/spl les/13 and R/spl les/6 are tabulated.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TIT.2005.860449</doi><tpages>5</tpages></addata></record> |
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| language | eng |
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| source | IEEE Electronic Library (IEL) |
| subjects | Applied sciences Codes Coding, codes Construction Covering Covering codes Data compression Error correction codes Exact sciences and technology Information theory Information, signal and communications theory Integer programming Linear programming Lower bounds Mathematical models Searching Signal and communications theory Tabu search Telecommunications and information theory unidirectional codes Upper bound Upper bounds |
| title | Unidirectional covering codes |
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