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.
|Title of host publication||Computing and combinatorics : 11th annual international conference, COCOON 2005, Kunming, Yunnan, China, August 16-19, 2005 : proceedings|
|Place of Publication||Berlin|
|Publication status||Published - 2005|
|Name||Lecture Notes in Computer Science|