On Codes Identifying Sets of Vertices in Hamming Spaces

AbstractA code $$C \subseteq F_2^n $$ is called (t, ≤2)-identifying if for all the words x, y(x ≠ y) and $$z$$ the sets (Bt(x) ⋃ Bt(y)) ⋂ C and $$B_t (z)\; \cap \;C$$ are nonempty and different. Constructions of such codes and a lower bound on the cardinality of these codes are given. The lower bound is shown to be sharp in some cases. We also discuss a more general notion of $$(t,\mathcal{F})$$ -identifying codes and introduce weakly identifying codes.