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

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