Error-set codes and related objects

A. Braeken, S.I. Nikova, V.S. Nikov

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

1 Citation (Scopus)

Abstract

By considering a new metric, Nikov and Nikova defined the class of error-set correcting codes. These codes differ from the error-correcting codes in the sense that the minimum distance of the code is replaced by a collection of monotone decreasing sets ¿ which define the supports of the vectors that do not belong to the code. In this paper we consider a subclass of these codes – so called, ideal codes – investigating their properties such as the relation with its dual and a formula for the weight enumerator. Next we show that the ¿-set of these codes corresponds to the independent sets of a matroid. Consequently, this completes the equivalence of ideal linear secret sharing schemes and matroids on one hand and linear secret sharing schemes and error-set correcting codes on the other hand.
Original languageEnglish
Title of host publicationComputing and combinatorics : 11th annual international conference, COCOON 2005, Kunming, Yunnan, China, August 16-19, 2005 : proceedings
EditorsL. Wang
Place of PublicationBerlin
PublisherSpringer
Pages577-585
ISBN (Print)3-540-28061-8
DOIs
Publication statusPublished - 2005

Publication series

NameLecture Notes in Computer Science
Volume3595
ISSN (Print)0302-9743

Cite this

Braeken, A., Nikova, S. I., & Nikov, V. S. (2005). Error-set codes and related objects. In L. Wang (Ed.), Computing and combinatorics : 11th annual international conference, COCOON 2005, Kunming, Yunnan, China, August 16-19, 2005 : proceedings (pp. 577-585). (Lecture Notes in Computer Science; Vol. 3595). Berlin: Springer. https://doi.org/10.1007/11533719_59
Braeken, A. ; Nikova, S.I. ; Nikov, V.S. / Error-set codes and related objects. Computing and combinatorics : 11th annual international conference, COCOON 2005, Kunming, Yunnan, China, August 16-19, 2005 : proceedings. editor / L. Wang. Berlin : Springer, 2005. pp. 577-585 (Lecture Notes in Computer Science).
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Braeken, A, Nikova, SI & Nikov, VS 2005, Error-set codes and related objects. in L Wang (ed.), Computing and combinatorics : 11th annual international conference, COCOON 2005, Kunming, Yunnan, China, August 16-19, 2005 : proceedings. Lecture Notes in Computer Science, vol. 3595, Springer, Berlin, pp. 577-585. https://doi.org/10.1007/11533719_59

Error-set codes and related objects. / Braeken, A.; Nikova, S.I.; Nikov, V.S.

Computing and combinatorics : 11th annual international conference, COCOON 2005, Kunming, Yunnan, China, August 16-19, 2005 : proceedings. ed. / L. Wang. Berlin : Springer, 2005. p. 577-585 (Lecture Notes in Computer Science; Vol. 3595).

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

TY - GEN

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N2 - By considering a new metric, Nikov and Nikova defined the class of error-set correcting codes. These codes differ from the error-correcting codes in the sense that the minimum distance of the code is replaced by a collection of monotone decreasing sets ¿ which define the supports of the vectors that do not belong to the code. In this paper we consider a subclass of these codes – so called, ideal codes – investigating their properties such as the relation with its dual and a formula for the weight enumerator. Next we show that the ¿-set of these codes corresponds to the independent sets of a matroid. Consequently, this completes the equivalence of ideal linear secret sharing schemes and matroids on one hand and linear secret sharing schemes and error-set correcting codes on the other hand.

AB - By considering a new metric, Nikov and Nikova defined the class of error-set correcting codes. These codes differ from the error-correcting codes in the sense that the minimum distance of the code is replaced by a collection of monotone decreasing sets ¿ which define the supports of the vectors that do not belong to the code. In this paper we consider a subclass of these codes – so called, ideal codes – investigating their properties such as the relation with its dual and a formula for the weight enumerator. Next we show that the ¿-set of these codes corresponds to the independent sets of a matroid. Consequently, this completes the equivalence of ideal linear secret sharing schemes and matroids on one hand and linear secret sharing schemes and error-set correcting codes on the other hand.

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Braeken A, Nikova SI, Nikov VS. Error-set codes and related objects. In Wang L, editor, Computing and combinatorics : 11th annual international conference, COCOON 2005, Kunming, Yunnan, China, August 16-19, 2005 : proceedings. Berlin: Springer. 2005. p. 577-585. (Lecture Notes in Computer Science). https://doi.org/10.1007/11533719_59