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It has been known that the code lengths of Tardos's collusion-secure fingerprinting codes are of theoretically minimal order with respect to the number of adversarial users (pirates). However, the code lengths can be further reduced, as some preceding studies on Tardos's codes already revealed. In this article we improve a recent discrete variant of(More)
We investigate candidates of finite random variables for c-secure random fingerprinting codes, in viewpoints of both code lengths and required memories. We determine, under a natural assumption, the random variables with the minimal number of outputs (i.e. optimal in a viewpoint of memory) among all candidates, by revealing their deep relation with theory(More)
A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. The main feature of this class of permutation codes, called linear programming (LP)-decodable permutation codes, is this LP decodability. It is demonstrated that the LP decoding performance of the proposed class of permutation codes is(More)
For designing low-density parity-check (LDPC) codes for quantum error-correction, we desire to satisfy the conflicting requirements below simultaneously. 1) The row weights of parity-check “should be large”: The minimum distances are bounded above by the minimum row weights of parity-check matrices of constituent classical codes. Small minimum(More)
In this paper, we consider quantum error correction over depolarizing channels with nonbinary low-density parity-check codes defined over Galois field of size 2<sup>p</sup>. The proposed quantum error correcting codes are based on the binary quasi-cyclic Calderbank, Shor, and Steane (CSS) codes. The resulting quantum codes outperform the best known quantum(More)
—Physical unclonable functions (PUFs) and biometrics are inherently noisy. When used in practice as cryptographic key generators, they need to be combined with an extraction technique to derive reliable bit strings (i.e., cryptographic key). An approach based on an error correcting code was proposed by Dodis et al. and is known as a fuzzy extractor.(More)