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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 1 of length n over a field extension F q m and its subcode C 2 C 1. One is called the relative dimension/intersection profile (RDIP), and the other is called the relative generalized rank weight (RGRW). We clarify their basic… (More)

—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)

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.

We show that the Feng-Rao bound for dual codes and a similar bound by Ander-sen and Geil [1] 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)

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)

SUMMARY We propose use of QR factorization with sort and Dijkstra'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 de-coder with small increase in the complexity required for… (More)

The information reconciliation in a quantum key distribution protocol can be studied separately from other steps in the protocol. The problem of information reconciliation can be reduced to that of distributed source coding. Its solution by LDPC codes is reviewed. We list some obstacles preventing the LDPC-based distributed source coding from becoming a… (More)

—The universal secure network coding presented by Silva et al. realizes secure and reliable transmission of a secret message over any underlying network code, by using maximum rank distance codes. Inspired by their result, this paper considers the secure network coding based on arbitrary linear codes, and investigates its security performance and error… (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)