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Journals and Conferences
The stabilizer code is the most general algebraic construction of quantum error-correcting codes proposed so far. A stabilizer code can be constructed from a self-orthogonal subspace of a symplectic space over a finite field. We propose a construction method of such a selforthogonal space using an algebraic curve. By using the proposed method we construct… (More)
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> ⊆ C<sub>1</sub>. One is called the relative dimension/intersection profile (RDIP), and the other is called the relative… (More)
which is called the L-construction, was not explicitly mentioned by Goppa but known to researchers including Goppa and Manin [17, p.386]. CL(D,mQ) seems to be first explicitly defined in , . Most research articles treat only CΩ(D,mQ). A reason for this trend may be due to the lack of efficient decoding algorithms for CL(D,mQ), while we know efficient… (More)
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.
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)
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… (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)
Under the assumption that we have defining equations of an affine algebraic curve in special position with respect to a rational place Q, we propose an algorithm computing a basis of L(D) of a divisor D from an ideal basis of the ideal L(D +∞Q) of the affine coordinate ring L(∞Q) of the given algebraic curve, where L(D+∞Q) := S∞ i=1 L(D+ iQ). Elements in… (More)
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 Gröbner basis conversion algorithm is performed at most dn logp de times in 2n variables, where d is the maximum of total degrees… (More)
We show universally attainable exponents for the decoding error and the mutual information and universally attainable equivocation rates for the conditional entropy for the broadcast channels with confidential messages. The error exponents are the same as ones given by Körner and Sgarro for the broadcast channels with degraded message sets.