Hφholdt, van Lint and Pellikaan proposed a generalization of one-point AG codes, called the evaluation codes. We show that an evaluation code from a weight function can be constructed as Miura's generalization of one-point AG codes. Hence we can construct a one-point AG code as good as a given evaluation code from a weight function.

Asymptotically good sequences of linear ramp secret sharing schemes have been intensively studied by Cramer et al. in terms of sequences of pairs of nested algebraic geometric codes [4]-[8], [10]. In those works the focus is on full privacy and full reconstruction. In this paper we analyze additional parameters describing the asymptotic behavior of partial information leakage and possibly also partial reconstruction giving a more complete picture of the access structure for sequences of linear ramp secret sharing schemes. Our study involves a detailed treatment of the (relative) generalized Hamming weights of the considered codes.

Source coding with a helper is one of the most fundamental fixed-length source coding problem for correlated sources. For this source coding, Wyner and Ahlswede-Korner showed the achievable rate region which is the set of rate pairs of encoders such that the probability of error can be made arbitrarily small for sufficiently large block length. However, their expression of the achievable rate region consists of the sum of indefinitely many sets. Thus, their expression is not useful for computing the achievable rate region. This paper deals with correlated sources whose conditional distribution is related by a binary-input output-symmetric channel, and gives a parametric form of the achievable rate region in order to compute the region easily.

We generalize the construction of quantum error-correcting codes from F4-linear codes by Calderbank et al. to pm-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.

Stabilizer-based quantum secret sharing has two methods to reconstruct a quantum secret: The erasure correcting procedure and the unitary procedure. It is known that the unitary procedure has a smaller circuit width. On the other hand, it is unknown which method has smaller depth and fewer circuit gates. In this letter, it is shown that the unitary procedure has smaller depth and fewer circuit gates than the erasure correcting procedure which follows a standard framework performing measurements and unitary operators according to the measurements outcomes, when the circuits are designed for quantum secret sharing using the [[5, 1, 3]] binary stabilizer code. The evaluation can be reversed if one discovers a better circuit for the erasure correcting procedure which does not follow the standard framework.

We introduce a coding theoretic criterion for Yamamoto's strong security of the ramp secret sharing scheme. After that, by using it, we show the strong security of the strongly multiplicative ramp secret sharing proposed by Chen et al. in 2008.

The multiple assignment scheme is to assign one or more shares to single participant so that any kind of access structure can be realized by classical secret sharing schemes. We propose its quantum version including ramp secret sharing schemes. Then we propose an integer optimization approach to minimize the average share size.

We propose two systematic constructions of deletion-correcting codes for protecting quantum inforomation. The first one works with qudits of any dimension l, which is referred to as l-adic, but only one deletion is corrected and the constructed codes are asymptotically bad. The second one corrects multiple deletions and can construct asymptotically good codes. The second one also allows conversion of stabilizer-based quantum codes to deletion-correcting codes, and entanglement assistance.

This paper surveys development of quantum error correction. With the familiarity with conventional coding theory and tensor product in multi-linear algebra, this paper can be read in a self-contained manner.

We show how to apply the Feng-Rao decoding algorithm and the Feng-Rao bound for the Ω-construction of algebraic geometry codes to the L-construction. Then we give examples in which the L-construction gives better linear codes than the Ω-construction in certain range of parameters on the same curve.

Secret sharing is a cryptographic scheme to encode a secret to multiple shares being distributed to participants, so that only qualified sets of participants can restore the original secret from their shares. When we encode a secret by a secret sharing scheme and distribute shares, sometimes not all participants are accessible, and it is desirable to distribute shares to those participants before a secret information is determined. Secret sharing schemes for classical secrets have been known to be able to distribute some shares before a given secret. Lie et al. found a ((2, 3))-threshold secret sharing for quantum secrets can distribute some shares before a given secret. However, it is unknown whether distributing some shares before a given secret is possible with other access structures of secret sharing for quantum secrets. We propose a quantum secret sharing scheme for quantum secrets that can distribute some shares before a given secret with other access structures.

In this paper, we present a lower bound for the dimension of subfield subcodes of residue Goppa codes on the curve Cab, which exceeds the lower bound given by Stichtenoth when the number of check symbols is not small. We also give an illustrative example which shows that the proposed bound for the dimension of certain residue Goppa code exceeds the true dimension of a BCH code with the same code length and designed distance.

We show a simple example of a secret sharing scheme encoding classical secret to quantum shares that can realize an access structure impossible by classical information processing with limitation on the size of each share. The example is based on quantum stabilizer codes.

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 decoder with small increase in the complexity required for preprocessing part of the decoder. Dijkstra's algorithm decreases the complexity of searching part of the decoder with increase in the storage complexity. The computer simulation demonstrates that the complexity of the decoder is reduced by the proposed methods significantly.

We show a construction of a quantum ramp secret sharing scheme from a nested pair of linear codes. Necessary and sufficient conditions for qualified sets and forbidden sets are given in terms of combinatorial properties of nested linear codes. An algebraic geometric construction for quantum secret sharing is also given.

We consider the problem of secret key agreement in Gaussian Maurer's Model. In Gaussian Maurer's model, legitimate receivers, Alice and Bob, and a wire-tapper, Eve, receive signals randomly generated by a satellite through three independent memoryless Gaussian channels respectively. Then Alice and Bob generate a common secret key from their received signals. In this model, we propose a protocol for generating a common secret key by using the result of soft-decision of Alice and Bob's received signals. Then, we calculate a lower bound on the secret key rate in our proposed protocol. As a result of comparison with the protocol that only uses hard-decision, we found that the higher rate is obtained by using our protocol.

When we have a singular Cab curve with many rational points, we had better to construct linear codes on its normalization rather than the original curve. The only obstacle to construct linear codes on the normalization is finding a basis of L( Q) having pairwise distinct pole orders at Q, where Q is the unique place of the Cab curve at infinity. We present an algorithm finding such a basis from defining equations of the normalization of the original Cab curve.

Low-density parity-check (LDPC) codes become very popular in channel coding, since they can achieve the performance close to maximum-likelihood (ML) decoding with linear complexity of the block length. Recently, Muramatsu et al. proposed a code using LDPC matrices for Slepian-Wolf source coding, and showed that their code can achieve any point in the achievable rate region of Slepian-Wolf source coding. However, since they employed ML decoding, their decoder needs to know the probability distribution of the source. Hence, it is an open problem whether there exists a universal code using LDPC matrices, where universal code means that the error probability of the code vanishes as the block length tends to infinity for all sources whose achievable rate region contains the rate pair of encoders. In this paper, we show the existence of a universal Slepian-Wolf source code using LDPC matrices for stationary memoryless sources.

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.

We consider the mismatched measurements in the BB84 quantum key distribution protocol, in which measuring bases are different from transmitting bases. We give a lower bound on the amount of a secret key that can be extracted from the mismatched measurements. Our lower bound shows that we can extract a secret key from the mismatched measurements with certain quantum channels, such as the channel over which the Hadamard matrix is applied to each qubit with high probability. Moreover, the entropic uncertainty principle implies that one cannot extract the secret key from both matched measurements and mismatched ones simultaneously, when we use the standard information reconciliation and privacy amplification procedure.