Separating Codes: Constructions and Bounds
نویسندگان
چکیده
Separating codes, initially introduced to test automaton, have revived lately in the study of fingerprinting codes, which are used for copyright protection. Separating codes play their role in making the fingerprinting scheme secure agains coalitions of pirates. We provide here better bounds, constructions and generalizations for these codes.
منابع مشابه
Improved bounds for separating hash families
An (N ;n,m, {w1, . . . , wt})-separating hash family is a set H of N functions h : X −→ Y with |X| = n, |Y | = m, t ≥ 2 having the following property. For any pairwise disjoint subsets C1, . . . , Ct ⊆ X with |Ci| = wi, i = 1, . . . , t, there exists at least one function h ∈ H such that h(C1), h(C2), . . . , h(Ct) are pairwise disjoint. Separating hash families generalize many known combinator...
متن کاملMore on -Separating Systems
The theory of separating systems has been applied in different areas of science and technology such as automata synthesis, technical diagnosis, and authenticating ownership claims. Constructions of (2 2)-separating systems derived from error-correcting codes are given, together with bounds on their parameters based on distance considerations.
متن کاملOn separating codes
Let Γ be a code of length n, and (T,U ) a pair of disjoint subsets of Γ. We say that (T,U ) is separated if there exists a coordinate i, such that for any codeword (c1, . . . , cn) ∈ T and any codeword (c ′ 1, . . . , c ′ n) ∈ U , ci 6= c ′ i. The code Γ is (t,u)-separating if all pairs (T,U ) with #T = t and #U = u are separated. Separating codes (or systems) are known from combinatorics, and ...
متن کاملOn optimal bounds for separating hash families
This paper concerns optimal bounds and constructions for separating hash families of type {1, w} and {2, 2}. We first prove optimal bounds for separating hash families of type {1, w} and show constructions of families achieving the bounds. As a by-product of the results we obtain a positive answer to a question put by Blackburn, Etzion, Stinson and Zaverucha recently. Next we study optimal boun...
متن کاملSeparating hash families: A Johnson-type bound and new constructions
Separating hash families are useful combinatorial structures which are generalizations of many well-studied objects in combinatorics, cryptography and coding theory. In this paper, using tools from graph theory and additive number theory, we solve several open problems and conjectures concerning bounds and constructions for separating hash families. Firstly, we discover that the cardinality of ...
متن کامل