Separating and Completely Separating Systems and Linear Codes

Abstract

In this correspondence, we present some more properties of separating systems (SS) and completely separating systems (CSS) from coding theory framework. First we derive the necessary and sufficient conditions for a set of vectors to be a SS or CSS. Then we show that in the case of linear codes, the necessary and sufficient conditions required for (1, 1) CSS are 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, we prove here that no linear code forms a(2, 1) or a(2, 2) CSS.