By extending the notion of minimum rank distance, this talk introduces two new relative code parameters of a linear code C_1 of length n over a field extension and its subcode C_2. One is called the relative dimension/intersection profile (RDIP), and the other is called the relative generalized rank weight (RGRW). We clarify their basic properties and the… (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)
We give an algorithm for constructing linear network error-correcting codes that achieve the Singleton bound for network error-correcting codes. The proposed algorithm is based on the algorithm by Jaggi et al. We also clarify the relationship between the robust network coding and the network error-correcting codes with known locations of errors.
—The secure multiplex coding (SMC) is a technique to remove rate loss in the coding for wire-tap 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… (More)
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 self-orthogonal space using an algebraic curve. By using the proposed method we construct… (More)
SUMMARY 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 Δ m of the secret vector s = [s 1 ,...,s l ] given m shares in terms of the RDLP of linear codes. We also characterize… (More)
We show that the Feng-Rao bound for dual codes and a similar bound by Ander-sen and Geil  for primary codes are consequences of each other. This implies that the Feng-Rao decoding algorithm can be applied to decode primary codes up to half their designed minimum distance. The technique applies to any linear code for which information on well-behaving… (More)
SUMMARY We generalize the construction of quantum error-correcting codes from F 4-linear codes by Calderbank et al. to p m-state systems. Then we show how to determine the error from a syndrome. Finally we discuss a systematic construction of quantum codes with efficient decoding algorithms.
SUMMARY We propose use of QR factorization with sort and Dijk-stra's algorithm for decreasing the computational complexity of the sphere decoder that is used for ML detection of signals on the multi-antenna fading channel. QR factorization with sort decreases the complexity of searching part of the decoder with small increase in the complexity required for… (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 n log p d times in 2n variables, where d is the maximum of total degrees of… (More)