A Note About the Traceability Properties of Linear Codes
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Auteurs : Marcel Fernandez [Espagne] ; Josep Cotrina [Espagne] ; Miguel Soriano [Espagne] ; Neus Domingo [Espagne]Source :
- 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
Affiliations:
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Barcelona</wicri:noRegion></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><affiliations><list><country><li>Espagne</li></country><region><li>Catalogne</li></region><settlement><li>Barcelone</li></settlement></list><tree><country name="Espagne"><region name="Catalogne"><name sortKey="Fernandez, Marcel" sort="Fernandez, Marcel" uniqKey="Fernandez M" first="Marcel" last="Fernandez">Marcel Fernandez</name></region><name sortKey="Cotrina, Josep" sort="Cotrina, Josep" uniqKey="Cotrina J" first="Josep" last="Cotrina">Josep Cotrina</name><name sortKey="Domingo, Neus" sort="Domingo, Neus" uniqKey="Domingo N" first="Neus" last="Domingo">Neus Domingo</name><name sortKey="Soriano, Miguel" sort="Soriano, Miguel" uniqKey="Soriano M" first="Miguel" last="Soriano">Miguel Soriano</name><name sortKey="Soriano, Miguel" sort="Soriano, Miguel" uniqKey="Soriano M" first="Miguel" last="Soriano">Miguel Soriano</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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