Ryutaroh Matsumoto

Construction Algorithm for Network Error-Correcting Codes Attaining the Singleton Bound

We give a centralized deterministic algorithm for constructing linear network error-correcting codes that attain the Singleton bound of network error-correcting codes. The proposed algorithm is based on the algorithm by Jaggi et al. We give estimates on the time complexity and the required symbol size of the proposed algorithm. We also estimate the probability of a random choice of local encoding vectors by all intermediate nodes giving a network error-correcting codes attaining the Singleton bound. We also clarify the relationship between the robust network coding and the network error-correcting codes with known locations of errors.

Improvement of Ashikhmin-Litsyn-Tsfasman bound for quantum codes

We improve performance of the asymptotically good quantum codes constructed by Ashikhmin, Litsyn, and Tsfasman (see Phys. Rev. A, vol.63, no.3, p.032311, Mar. 2001), by using more rational points on algebraic curves.

Secure multiplex coding with dependent and non-uniform multiple messages

The secure multiplex coding (SMC) is a technique to remove rate loss in the coding for wiretap channels and broadcast channels with confidential messages caused by the inclusion of random bits into transmitted signals. SMC replaces the random bits by other meaningful secret messages, and a collection of secret messages serves as the random bits to hide the rest of messages. In the previous researches, multiple secret messages were assumed to have independent and uniform distributions, which is difficult to be ensured in practice. We remove this restrictive assumption by a generalization of the channel resolvability technique.

Construction of wiretap codes from ordinary channel codes

From an arbitrary given channel code over a discrete or Gaussian memoryless channel, we construct a wiretap code with the strong security. Our construction can achieve the wiretap capacity under mild assumptions. The key tool is the new privacy amplification theorem bounding the eavesdropped information in terms of the Gallager function.

Tomography increases key rates of quantum-key-distribution protocols

We construct a practically implementable classical processing for the Bennett-Brassard 1984 (BB84) protocol and the six-state protocol that fully utilizes the accurate channel estimation method, which is also known as the quantum tomography. Our proposed processing yields at least as high a key rate as the standard processing by Shor and Preskill. We show two examples of quantum channels over which the key rate of our proposed processing is strictly higher than the standard processing. In the second example, the BB84 protocol with our proposed processing yields a positive key rate even though the so-called error rate is higher than the 25% limit.

Strongly secure privacy amplification cannot be obtained by encoder of Slepian-Wolf code

The privacy amplification is a technique to distill a secret key from a random variable by a hash function so that the distilled key and an eavesdroppers random variable is statistically independent. There are two kinds of security criteria for the key distilled by the privacy amplification: the weak security criterion and the strong security criterion. As a technique to distill a secret key, it is known that the encoder of a Slepian-Wolf (the source coding with full side-information at the decoder) code can be used as a hash function for the privacy amplification if we employ the weak security criterion. In this paper, we show that the encoder of a Slepian-Wolf code cannot be used as a hash function for the privacy amplification if we employ the strong security criterion.

Relative generalized Hamming weights of one-point algebraic geometric codes

Security of linear ramp secret sharing schemes can be characterized by the relative generalized Hamming weights of the involved codes [23], [22]. In this paper we elaborate on the implication of these parameters and we devise a method to estimate their value for general one-point algebraic geometric codes. As it is demonstrated, for Hermitian codes our bound is often tight. Furthermore, for these codes the relative generalized Hamming weights are often much larger than the corresponding generalized Hamming weights.

Secure Multiplex Network Coding

In the secure network coding for multicasting, there is loss of information rate due to inclusion of random bits at the source node. We show a method to eliminate that loss of information rate by using multiple statistically independent messages to be kept secret from an eavesdropper. The proposed scheme is an adaptation of Yamamoto et al.s secure multiplex coding to the secure network coding.

Secure Multiplex Coding With Dependent and Non-Uniform Multiple Messages

The secure multiplex coding (SMC) is a technique to remove rate loss in the coding for wiretap channels and broadcast channels with confidential messages caused by the inclusion of random bits into transmitted signals. SMC replaces the random bits by other meaningful secret messages, and a collection of secret messages serves as the random bits to hide the rest of messages. In the previous researches, multiple secret messages were assumed to have independent and uniform distributions, which is difficult to be ensured in practice. We remove this restrictive assumption by a generalization of the channel resolvability technique.

Computing the Radical of an Ideal in Positive Characteristic

We propose a method for computing the radical of an arbitrary ideal in the polynomial ring in n variables over a perfect field of characteristic p 0. In our method Buchberger?s algorithm is performed once in n variables and a Grobner basis conversion algorithm is performed at most ?nlogpd? times in 2 n variables, where d is the maximum of total degrees of generators of the ideal and 3. Next we explain how to compute radicals over a finitely generated coefficient field over a field K, when we have a radical computation method over the field K. Thus we can compute radicals over any finitely generated field over a perfect field.