Tomohiko Uyematsu

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By extending the notion of minimum rank distance, this paper introduces two new relative code parameters of a linear code C<sub>1</sub> of length n over a field extension F<sub>q</sub><sup>m</sup> and its subcode C<sub>2</sub> &#x2286; C<sub>1</sub>. One is called the relative dimension/intersection profile (RDIP), and the other is called the relative(More)
We generalize the random coding argument of stabilizer codes and derive a lower bound on the quantum capacity of an arbitrary discrete memoryless quantum channel. For the depolarizing channel, our lower bound coincides with that obtained by Bennett et al. We also slightly improve the quantum Gilbert–Varshamov bound for general stabilizer codes, and(More)
This paper precisely characterizes secret sharing schemes based on arbitrary linear codes by using the relative dimension/length profile (RDLP) and the relative generalized Hamming weight (RGHW). We first describe the equivocation Δm of the secret vector s = [s1, . . . ,sl ] given m shares in terms of the RDLP of linear codes. We also characterize two(More)
Quantum error-correcting codes have attracted much attention. Among many research articles, the most general and systematic construction is the so called stabilizer code construction [6] or additive code construction [2], which constructs a quantum error-correcting code as an eigenspace of an Abelian subgroup S of the error group. Thereafter Calderbank et(More)
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 eavesdropper's 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(More)
Let N(d,d<sup>perp</sup>) denote the minimum length n of a linear code C with d and d<sup>perp</sup>, where d is the minimum Hamming distance of C and d<sup>perp</sup> is the minimum Hamming distance of C<sup>perp</sup>. In this correspondence, we show lower bounds and an upper bound on N(d,d<sup>perp</sup>). Further, for small values of d and(More)
The universal strongly secure network coding scheme allows communication at maximum rate while ensuring that, independently from the underlying network code, no part of the secret message is revealed to the wiretapper. Although Silva and Kschischang showed the existence of such a scheme, the explicit construction remained an open question. This paper(More)
Linear codes for a coding problem of correlated sources are considered. It is proved that we can construct codes by using low-density parity-check (LDPC) matrices with maximum-likelihood (or typical set) decoding. As applications of the above coding problem, a construction of codes is presented for multiple-access channel with correlated additive noises and(More)