Separating and Completely Separating Systems and Linear Codes.

摘要

In this report the authors establish the necessary and sufficient conditions for a set of vectors to be a separating system (SS) or a completely separating system (CSS) from coding theory framework. It is shown that, in the case of linear codes the necessary and sufficient condition required for (1,1) CSS is similar to that of (2,1) SS and by deleting the 0 vector from a binary code that forms a (2,1) SS, the set of remaining code words forms a (1,1) CSS. Even though some linear codes form (2,1) and (2,2) SS, it is proven here that no linear code forms a (2,1) or a (2,2) CSS. (Author)