This paper presents private information retrieval (PIR) schemes for coded storage with colluding servers, which are not restricted to maximum distance separable (MDS) codes. PIR schemes for general linear codes are constructed and the resulting PIR rate is calculated explicitly. It is shown that codes with transitive automorphism groups yield the highest possible rates obtainable with the propo...

We consider the Maxwell-Stefan model of diffusion in a multicomponent gaseous mixture. After focusing on the main differences with the Fickian diffusion model, we study the equations governing a three-component gas mixture. Mostly in the case of a tridiagonal diffusion matrix, we provide a qualitative and quantitative mathematical analysis of the model. We develop moreover a standard explicit n...

Many modern block ciphers use maximum distance separate (MDS) matrices as their diffusion layers. In this paper, we propose a new method to verify a sort of MDS diffusion block matrices whose blocks are all polynomials in a certain primitive block over the finite field F2. And then we discover a new kind of transformations that can retain MDS property of diffusion matrices and generate a series...

2014 The general results recently obtained for the Boltzmann collision term in a gas of atomic hydrogen are applied to the study of longitudinal spin diffusion in high magnetic fields. This phenomenon can be described as a diffusion of concentration in a four component reactive mixture (the reaction being here the electronic transfer between nuclei). A numerical discussion of all the coefficien...

We study the stability of explicit one-step integration schemes for the linear finite element approximation of linear parabolic equations. The derived bound on the largest permissible time step is tight for any mesh and any diffusion matrix within a factor of 2(d + 1), where d is the spatial dimension. Both full mass matrix and mass lumping are considered. The bound reveals that the stability c...

We generalize the total variation restoration model, introduced by Rudin, Osher, and Fatemi in 1992, to matrix-valued data, in particular, to diffusion tensor images (DTIs). Our model is a natural extension of the color total variation model proposed by Blomgren and Chan in 1998. We treat the diffusion matrix D implicitly as the product D = LL(T), and work with the elements of L as variables, i...

The paper examines a class of first order linear hyperbolic systems, proposed as a generalization of the Goldstein–Kac model for velocity-jump processes and determined by a finite number of speeds and corresponding transition rates. It is shown that the large-time behavior is described by a corresponding scalar diffusive equation of parabolic type, defined by a diffusion matrix for which an exp...

Upper bounds on Kq (n; R), the minimum number of codewords in a q-ary code of length n and covering radius R, are improved. Such bounds are obtained by constructing corresponding covering codes. In particular, codes of length q + 1 are discussed. Good such codes can be obtained from maximum distance separable (MDS) codes. Furthermore, they can often be combined eeectively with other covering co...

A q-ary maximum distance separable (MDS) code C with length n, dimension k over an alphabet A of size q is a set of qk codewords that are elements of An, such that the Hamming distance between two distinct codewords in C is at least n− k+1. Sets of mutually orthogonal Latin squares of orders q ≤ 9, corresponding to two-dimensional q-ary MDS codes, and q-ary one-error-correcting MDS codes for q ...