In this work, we study the tradeoffs between the error probabilities of classical-quantum channels and the blocklength n when the transmission rates approach the channel capacity at a rate slower than 1/ √ n, a research topic known as moderate deviation analysis. We show that the optimal error probability vanishes under this rate convergence. Our main technical contributions are a tight quantum...

Error-correcting pairs were introduced in 1988 in the pre-print [24] that appeared in [26], and were found independently in [18], as a general algebraic method of decoding linear codes. These pairs exist for several classes of codes. However little or no study has been made for characterizing those codes. This article is an attempt to fill the vacuum left by the literature concerning this subje...

The doubly shortened perfect codes of length 13 are classified utilizing the classification of perfect codes in [P.R.J. Österg̊ard and O. Pottonen, The perfect binary one-error-correcting codes of length 15: Part I— Classification, IEEE Trans. Inform. Theory, to appear]; there are 117821 such (13,512,3) codes. By applying a switching operation to those codes, two more (13,512,3) codes are obtain...

In error-correcting codes for combating noisy transmission channels, a central concept i s the notion of minimum distance. If a code can be constructed with minimum distance between code points of 2m-k 1 I then any number of errors per code word which does not exceed m can be corrected, thus increasing the reliability of transmission above that to be expected with no redundancy i n the code. An...

Properties of the three-nucleon bound state are examined in the Faddeev formalism, in which the quark-model nucleon-nucleon interaction is explicitly incorporated to calculate the off-shell T -matrix. The most recent version, fss2, of the Kyoto-Niigata quark-model potential yields the ground-state energy E(3H) = −8.514 MeV in the 34 channel calculation, when the np interaction is used for the n...

Both MDS and Euclidean self-dual codes have theoretical and practical importance and the study of MDS self-dual codes has attracted lots of attention in recent years. In particular, determining existence of q-ary MDS self-dual codes for various lengths has been investigated extensively. The problem is completely solved for the case where q is even. The current paper focuses on the case where q ...

In this paper, we apply Legendre wavelet collocation method to obtain the approximate solution of nonlinear Stratonovich Volterra integral equations. The main advantage of this method is that Legendre wavelet has orthogonality property and therefore coefficients of expansion are easily calculated. By using this method, the solution of nonlinear Stratonovich Volterra integral equation reduces to...

We study the problem of existence of (nontrivial) perfect codes in the discrete n-simplex ∆` := {( x0, . . . , xn ) : xi ∈ Z+, ∑ i xi = ` } under `1 metric. The problem is motivated by the so-called multiset codes, which have recently been introduced by the authors as appropriate constructs for error correction in the permutation channels. It is shown that e-perfect codes in the 1-simplex ∆` ex...

We study the large deviations performance of consensus+innovations distributed detection over random networks, where each sensor, at each time k, weight averages its decision variable with its neighbors decision variables (consensus), and accounts for its new observation (innovation). Sensor observations are independent identically distributed (i.i.d.) both in time and space, but have generic (...

We study properties of rank metric and codes in rank metric over finite fields. We show that perfect codes do not exist. We derive an equivalent of the Varshamov-Gilbert bound in Hamming metric. We study the asymptotic behavior of the minimum rank distance of codes that are on GV. We show that the packing density of maximum rank distance codes is lower bounded by a function depending on the err...