A Note About the Traceability Properties of Linear Codes
Identifieur interne : 005773 ( Istex/Corpus ); précédent : 005772; suivant : 005774A Note About the Traceability Properties of Linear Codes
Auteurs : Marcel Fernandez ; Josep Cotrina ; Miguel Soriano ; Neus DomingoSource :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2007.
Abstract
Abstract: We characterize the traceability properties of linear codes. It is well known that any code of length n and minimum distance d is a c-TA code if c 2 < n/(n − d). In this paper, we show that a less restrictive condition can be derived. In other words, there exists a value Z C , with n − d ≤ Z C ≤ c(n − d), such that any linear code is c-TA if c < n/Z C . We also prove that in many cases this condition is also necessary. These results are applied to cyclic and Reed-Solomon codes.
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DOI: 10.1007/978-3-540-76788-6_20
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Barcelona, Spain</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="s">Lecture Notes in Computer Science</title><imprint><date>2007</date></imprint><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="ISSN">0302-9743</idno></series><idno type="istex">079E810651163439484C957B9342E895E57AB0FB</idno><idno type="DOI">10.1007/978-3-540-76788-6_20</idno><idno type="ChapterID">20</idno><idno type="ChapterID">Chap20</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: We characterize the traceability properties of linear codes. It is well known that any code of length n and minimum distance d is a c-TA code if c 2 < n/(n − d). In this paper, we show that a less restrictive condition can be derived. In other words, there exists a value Z C , with n − d ≤ Z C ≤ c(n − d), such that any linear code is c-TA if c < n/Z C . We also prove that in many cases this condition is also necessary. These results are applied to cyclic and Reed-Solomon codes.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>Marcel Fernandez</name><affiliations><json:string>Technical University of Catalonia, Department of Telematic Engineering, C/Jordi Girona 1-3, C3 08034, Barcelona, Spain</json:string></affiliations></json:item><json:item><name>Josep Cotrina</name><affiliations><json:string>Technical University of Catalonia, Department of Telematic Engineering, C/Jordi Girona 1-3, C3 08034, Barcelona, Spain</json:string></affiliations></json:item><json:item><name>Miguel Soriano</name><affiliations><json:string>Technical University of Catalonia, Department of Telematic Engineering, C/Jordi Girona 1-3, C3 08034, Barcelona, Spain</json:string><json:string>CTTC. Centre Tecnolgic de Telecomunicacions de Catalunya, Av. Canal Olímpic S/N 08860 - Castelldefels. Barcelona, Spain</json:string></affiliations></json:item><json:item><name>Neus Domingo</name><affiliations><json:string>I.E.S. J.V Foix, Rubi. Barcelona, Spain</json:string></affiliations></json:item></author><language><json:string>eng</json:string></language><abstract>Abstract: We characterize the traceability properties of linear codes. It is well known that any code of length n and minimum distance d is a c-TA code if c 2 > n/(n − d). In this paper, we show that a less restrictive condition can be derived. In other words, there exists a value Z C , with n − d ≤ Z C ≤ c(n − d), such that any linear code is c-TA if c > n/Z C . We also prove that in many cases this condition is also necessary. 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It is well known that any code of length n and minimum distance d is a c-TA code if c 2 < n/(n − d). In this paper, we show that a less restrictive condition can be derived. In other words, there exists a value Z C , with n − d ≤ Z C ≤ c(n − d), such that any linear code is c-TA if c < n/Z C . We also prove that in many cases this condition is also necessary. 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Proceedings</BookSubTitle><BookVolumeNumber>4817</BookVolumeNumber><BookSequenceNumber>4817</BookSequenceNumber><BookDOI>10.1007/978-3-540-76788-6</BookDOI><BookTitleID>158070</BookTitleID><BookPrintISBN>978-3-540-76787-9</BookPrintISBN><BookElectronicISBN>978-3-540-76788-6</BookElectronicISBN><BookChapterCount>28</BookChapterCount><BookCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2007</CopyrightYear></BookCopyright><BookSubjectGroup><BookSubject Code="I" Type="Primary">Computer Science</BookSubject><BookSubject Code="I15033" Priority="1" Type="Secondary">Data Encryption</BookSubject><BookSubject Code="I17028" Priority="2" Type="Secondary">Discrete Mathematics in Computer Science</BookSubject><BookSubject Code="I14050" Priority="3" Type="Secondary">Systems and Data Security</BookSubject><BookSubject Code="I24067" Priority="4" Type="Secondary">Management of Computing and Information Systems</BookSubject><BookSubject Code="I16021" Priority="5" Type="Secondary">Algorithm Analysis and Problem Complexity</BookSubject><BookSubject Code="I13022" Priority="6" Type="Secondary">Computer Communication Networks</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup></BookInfo><BookHeader><EditorGroup><Editor><EditorName DisplayOrder="Western"><GivenName>Kil-Hyun</GivenName><FamilyName>Nam</FamilyName></EditorName><Contact><Email>khnam@kndu.ac.kr</Email></Contact></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>Gwangsoo</GivenName><FamilyName>Rhee</FamilyName></EditorName><Contact><Email>rhee@sookmyung.ac.kr</Email></Contact></Editor></EditorGroup></BookHeader><Part ID="Part3"><PartInfo TocLevels="0"><PartID>3</PartID><PartSequenceNumber>3</PartSequenceNumber><PartTitle>Hash Functions – I</PartTitle><PartChapterCount>9</PartChapterCount><PartContext><SeriesID>558</SeriesID><BookTitle>Information Security and Cryptology - ICISC 2007</BookTitle></PartContext></PartInfo><SubPart ID="SubPart6"><SubPartInfo><SubPartID>6</SubPartID><SubPartSequenceNumber>6</SubPartSequenceNumber><SubPartTitle>Copyright Protection</SubPartTitle><SubPartChapterCount>1</SubPartChapterCount></SubPartInfo><Chapter ID="Chap20" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingStyle="Unnumbered" TocLevels="0"><ChapterID>20</ChapterID><ChapterDOI>10.1007/978-3-540-76788-6_20</ChapterDOI><ChapterSequenceNumber>20</ChapterSequenceNumber><ChapterTitle Language="En">A Note About the Traceability Properties of Linear Codes</ChapterTitle><ChapterFirstPage>251</ChapterFirstPage><ChapterLastPage>258</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2007</CopyrightYear></ChapterCopyright><ChapterGrants Type="Regular"><MetadataGrant Grant="OpenAccess"></MetadataGrant><AbstractGrant Grant="OpenAccess"></AbstractGrant><BodyPDFGrant Grant="Restricted"></BodyPDFGrant><BodyHTMLGrant Grant="Restricted"></BodyHTMLGrant><BibliographyGrant Grant="Restricted"></BibliographyGrant><ESMGrant Grant="Restricted"></ESMGrant></ChapterGrants><ChapterContext><SeriesID>558</SeriesID><PartID>3</PartID><BookID>978-3-540-76788-6</BookID><BookTitle>Information Security and Cryptology - ICISC 2007</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Marcel</GivenName><FamilyName>Fernandez</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Josep</GivenName><FamilyName>Cotrina</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff1 Aff2"><AuthorName DisplayOrder="Western"><GivenName>Miguel</GivenName><FamilyName>Soriano</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff3"><AuthorName DisplayOrder="Western"><GivenName>Neus</GivenName><FamilyName>Domingo</FamilyName></AuthorName></Author><Affiliation ID="Aff1"><OrgName>Technical University of Catalonia, Department of Telematic Engineering, C/Jordi Girona 1-3, C3 08034, Barcelona</OrgName><OrgAddress><Country>Spain</Country></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgName>CTTC. Centre Tecnolgic de Telecomunicacions de Catalunya, Av. Canal Olímpic S/N 08860 - Castelldefels. Barcelona</OrgName><OrgAddress><Country>Spain</Country></OrgAddress></Affiliation><Affiliation ID="Aff3"><OrgName>I.E.S. J.V Foix, Rubi. Barcelona</OrgName><OrgAddress><Country>Spain</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>We characterize the traceability properties of linear codes. It is well known that any code of length <Emphasis Type="Italic">n</Emphasis> and minimum distance <Emphasis Type="Italic">d</Emphasis> is a <Emphasis Type="Italic">c</Emphasis>-TA code if <Emphasis Type="Italic">c</Emphasis><Superscript>2</Superscript> < <Emphasis Type="Italic">n</Emphasis>/(<Emphasis Type="Italic">n</Emphasis> − <Emphasis Type="Italic">d</Emphasis>). In this paper, we show that a less restrictive condition can be derived. In other words, there exists a value <Emphasis Type="Italic">Z</Emphasis><Subscript><Emphasis Type="Italic">C</Emphasis></Subscript>, with <Emphasis Type="Italic">n</Emphasis> − <Emphasis Type="Italic">d</Emphasis> ≤ <Emphasis Type="Italic">Z</Emphasis><Subscript><Emphasis Type="Italic">C</Emphasis></Subscript> ≤ <Emphasis Type="Italic">c</Emphasis>(<Emphasis Type="Italic">n</Emphasis> − <Emphasis Type="Italic">d</Emphasis>), such that any linear code is <Emphasis Type="Italic">c</Emphasis>-TA if <Emphasis Type="Italic">c</Emphasis> < <Emphasis Type="Italic">n</Emphasis>/<Emphasis Type="Italic">Z</Emphasis><Subscript><Emphasis Type="Italic">C</Emphasis></Subscript>. We also prove that in many cases this condition is also necessary. These results are applied to cyclic and Reed-Solomon codes.</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></SubPart></Part></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>A Note About the Traceability Properties of Linear Codes</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>A Note About the Traceability Properties of Linear Codes</title></titleInfo><name type="personal"><namePart type="given">Marcel</namePart><namePart type="family">Fernandez</namePart><affiliation>Technical University of Catalonia, Department of Telematic Engineering, C/Jordi Girona 1-3, C3 08034, Barcelona, Spain</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Josep</namePart><namePart type="family">Cotrina</namePart><affiliation>Technical University of Catalonia, Department of Telematic Engineering, C/Jordi Girona 1-3, C3 08034, Barcelona, Spain</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Miguel</namePart><namePart type="family">Soriano</namePart><affiliation>Technical University of Catalonia, Department of Telematic Engineering, C/Jordi Girona 1-3, C3 08034, Barcelona, Spain</affiliation><affiliation>CTTC. Centre Tecnolgic de Telecomunicacions de Catalunya, Av. Canal Olímpic S/N 08860 - Castelldefels. Barcelona, Spain</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Neus</namePart><namePart type="family">Domingo</namePart><affiliation>I.E.S. J.V Foix, Rubi. Barcelona, Spain</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">2007</dateIssued><copyrightDate encoding="w3cdtf">2007</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">Abstract: We characterize the traceability properties of linear codes. It is well known that any code of length n and minimum distance d is a c-TA code if c 2 < n/(n − d). In this paper, we show that a less restrictive condition can be derived. In other words, there exists a value Z C , with n − d ≤ Z C ≤ c(n − d), such that any linear code is c-TA if c < n/Z C . We also prove that in many cases this condition is also necessary. These results are applied to cyclic and Reed-Solomon codes.</abstract><relatedItem type="host"><titleInfo><title>Information Security and Cryptology - ICISC 2007</title><subTitle>10th International Conference, Seoul, Korea, November 29-30, 2007. Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">Kil-Hyun</namePart><namePart type="family">Nam</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Gwangsoo</namePart><namePart type="family">Rhee</namePart><role><roleTerm type="text">editor</roleTerm></role></name><genre type="Book Series" displayLabel="Proceedings"></genre><originInfo><copyrightDate encoding="w3cdtf">2007</copyrightDate><issuance>monographic</issuance></originInfo><subject><genre>Book Subject Collection</genre><topic authority="SpringerSubjectCodes" authorityURI="SUCO11645">Computer Science</topic></subject><subject><genre>Book Subject Group</genre><topic authority="SpringerSubjectCodes" authorityURI="I">Computer Science</topic><topic authority="SpringerSubjectCodes" authorityURI="I15033">Data Encryption</topic><topic authority="SpringerSubjectCodes" authorityURI="I17028">Discrete Mathematics in Computer Science</topic><topic 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type="family">Weikum</namePart><role><roleTerm type="text">editor</roleTerm></role></name><originInfo><copyrightDate encoding="w3cdtf">2007</copyrightDate><issuance>serial</issuance></originInfo><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="SeriesID">558</identifier><recordInfo><recordOrigin>Springer-Verlag Berlin Heidelberg, 2007</recordOrigin></recordInfo></relatedItem><identifier type="istex">079E810651163439484C957B9342E895E57AB0FB</identifier><identifier type="DOI">10.1007/978-3-540-76788-6_20</identifier><identifier type="ChapterID">20</identifier><identifier type="ChapterID">Chap20</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag Berlin Heidelberg, 2007</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Springer-Verlag Berlin Heidelberg, 2007</recordOrigin></recordInfo></mods></metadata></istex></record>Pour manipuler ce 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