Upper Bounds on the Number of Codewords of Some Separating Codes
This work addresses theoretical limits in coding theory for applications like digital fingerprinting, but it appears incremental as it builds on existing conjectures and focuses on specific code types.
The paper tackles the problem of establishing upper bounds on the number of codewords in separating codes, which are used in collusion-secure fingerprinting, by proposing new bounds for restricted separating codes and proving that the Upper Bound Conjecture holds for almost all Reed-Solomon 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.