Improved constructions of nested code pairs

Carlos Galindo; Hans Olav Geil; Fernando Hernando; Diego Ruano Benito

doi:10.1109/TIT.2017.2755682

Improved constructions of nested code pairs

Carlos Galindo, Hans Olav Geil, Fernando Hernando, Diego Ruano Benito

Research output: Contribution to journal › Journal article › Research › peer-review

12 Citations (Scopus)

Abstract

Two new constructions of linear code pairs C₂ ⊂ C₁ are given for which the codimension and the relative minimum distances M ₁ (C ₁ , C ₂ ) and 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. They can also be used to ensure reliable communication over asymmetric quantum channels. The new constructions result from carefully applying the Feng-Rao bounds to a family of codes defined from multivariate polynomials and Cartesian product point sets.

Original language	English
Journal	I E E E Transactions on Information Theory
Volume	64
Issue number	4
Pages (from-to)	2444-2459
Number of pages	16
ISSN	0018-9448
DOIs	https://doi.org/10.1109/TIT.2017.2755682
Publication status	Published - 1 Apr 2018

Keywords

Asymmetric quantum code
CSS construction
Feng-Rao bound
nested codes
ramp secret sharing
relative generalized Hamming weight
relative minimum distance
wiretap channel of type II

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10.1109/TIT.2017.2755682

https://arxiv.org/pdf/1610.06363v2.pdf

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AU - Geil, Hans Olav

AU - Hernando, Fernando

AU - Ruano Benito, Diego

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AB - Two new constructions of linear code pairs C 2 ⊂ C 1 are given for which the codimension and the relative minimum distances M 1 (C 1 , C 2 ) and M 1 (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. They can also be used to ensure reliable communication over asymmetric quantum channels. The new constructions result from carefully applying the Feng-Rao bounds to a family of codes defined from multivariate polynomials and Cartesian product point sets.

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KW - CSS construction

KW - Feng-Rao bound

KW - nested codes

KW - ramp secret sharing

KW - relative generalized Hamming weight

KW - relative minimum distance

KW - wiretap channel of type II

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Improved constructions of nested code pairs

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