Upper Bounds on the Number of Codewords of Some Separating Codes
Ryul Kim, Myong-Son Sin, Ok-Hyon Song
TL;DR
This paper investigates upper bounds on the number of codewords in separating codes, providing new bounds for restricted codes and confirming a conjecture for Reed-Solomon codes, with implications for digital fingerprinting and group testing.
Contribution
It introduces new upper bounds for restricted separating codes and verifies the Upper Bound Conjecture for most Reed-Solomon codes, advancing theoretical understanding.
Findings
New upper bounds for restricted separating codes
Confirmation of the Upper Bound Conjecture for most Reed-Solomon codes
Implications for digital fingerprinting and related structures
Abstract
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.
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Taxonomy
TopicsAdvanced Steganography and Watermarking Techniques · graph theory and CDMA systems · Cryptography and Data Security