Improved constructions of nested code pairs
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Other documents of the author: Galindo, Carlos; Geil, Olav; Hernando, Fernando; Ruano, Diego
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comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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Title
Improved constructions of nested code pairsDate
2017-09Publisher
IEEEBibliographic citation
GALINDO, Carlos, et al. Improved constructions of nested code pairs. IEEE Transactions on Information Theory, 2017.Type
info:eu-repo/semantics/articlePublisher version
http://ieeexplore.ieee.org/abstract/document/8048519/Version
info:eu-repo/semantics/submittedVersionSubject
Abstract
Two new constructions of linear code pairs C2 ⊂ C1 are given for which the codimension and the relative minimum distances M1(C1,C2), M1(C┴2 , C┴1) are good. By this we mean that for any two out of the three parameters ... [+]
Two new constructions of linear code pairs C2 ⊂ C1 are given for which the codimension and the relative minimum distances M1(C1,C2), M1(C┴2 , C┴1) are good. By this we mean that for any two out of the three parameters the third parameter of the constructed code pair is large. Such pairs of nested codes are indispensable for the determination of good linear ramp secret sharing schemes [40]. They can also be used to ensure reliable communication over asymmetric quantum channels [54]. The new constructions result from carefully applying the Feng-Rao bounds [21], [31] to a family of codes defined from multivariate polynomials and Cartesian product point sets. [-]
Investigation project
The Danish Council for Independent Research (Grant No. DFF–4002-00367); Spanish MINECO/FEDER (Grants No. MTM2015-65764-C2-2-P and MTM2015-69138-REDT); University Jaume I (Grant No. P1-1B2015-02)Rights
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