Upper Bounds on the Number of Codewords of Some Separating Codes

Separating codes have their applications in collusion-secure fingerprinting for generic digital data, while they are also related to the other structures including hash family, intersection code and group testing. In this paper we study upper bounds for separating codes. First, some new upper bound for restricted separating codes is proposed. Then we illustrate that the Upper Bound Conjecture for separating Reed-Solomon codes inherited from Silverberg’s question holds true for almost all Reed-Solomon codes.

💡 Research Summary

The paper investigates upper bounds on the size of separating codes, a class of error‑correcting codes that guarantee that two distinct sets of users cannot produce the same set of verification symbols. Such codes are central to collusion‑secure fingerprinting, hash families, intersection codes, and group testing. The authors make two principal contributions.

First, they derive a new combinatorial upper bound for restricted separating codes, where each codeword is constrained to a prescribed alphabet subset. By counting the number of ways a set of w codewords can fail to be separated and the number of ways a set of ℓ codewords can be correctly separated, they obtain

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