Error-Set Codes and Related Objects | Zendy

An Braeken | Zendy; Ventzislav Nikov | Zendy; ⋆Svetla Nikova | Zendy

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Error-Set Codes and Related Objects

Author(s) -

An Braeken,

Ventzislav Nikov,

⋆Svetla Nikova

Publication year - 2005

Publication title -

lecture notes in computer science

Language(s) - English

Resource type - Book series

SCImago Journal Rank - 0.249

H-Index - 400

eISSN - 1611-3349

pISSN - 0302-9743

ISBN - 3-540-28061-8

DOI - 10.1007/11533719_59

Subject(s) - matroid , discrete mathematics , linear code , ideal (ethics) , computer science , secret sharing , set (abstract data type) , equivalence relation , mathematics , class (philosophy) , code (set theory) , monotone polygon , block code , algorithm , cryptography , decoding methods , philosophy , epistemology , artificial intelligence , programming language , geometry

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 Δ 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 Δ-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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