The Cryptographics Algorithms AES and Twofish guarantee a high diffusion with the use of fixed MDS matrices of size 4 × 4. In this article variations to the Cryptographics Algorithms AES and Twofish are made. They allow that the process of cipher decipher come true with MDS matrices selected randomly from an algorithm that obtaining an MDS matrix of set of all the MDS matrices possible. A new S...

Recently, Yaakobi et al. introduced codes for b-symbol read channels, where the read operation is performed as a consecutive sequence of b > 2 symbols. In this paper, we establish a Singleton-type bound on b-symbol codes. Codes meeting the Singleton-type bound are called maximum distance separable (MDS) codes, and they are optimal in the sense they attain the maximal minimum bdistance. Based on...

Multidimensional Scaling (MDS) is a classical technique for embedding data in low dimensions, still widespread use today. In this paper we study MDS modern setting - specifically, high dimensions and ambient measurement noise. We show that as the noise level increases, suffers sharp breakdown depends on dimension level, derive an explicit formula point case of white then introduce MDS+, simple ...

– Consider uniformly elliptic random walk on Z with independent jump rates across nearest neighbour bonds of the lattice. We show that the infinite volume effective diffusion matrix can be almost surely recovered as the limit of finite volume periodized effective diffusion matrices.  2003 Éditions scientifiques et médicales Elsevier SAS MSC: 60K37; 60K35; 74Q20

The notion of universally decodable matrices (UDMs) was recently introduced by Tavildar and Viswanath while studying slow fading channels. It turns out that the problem of constructing UDMs is tightly connected to the problem of constructing maximum distance separable (MDS) codes. In this paper, we first study the properties of UDMs in general and then we discuss an explicit construction of a c...

The GM-MDS conjecture of Dau et al. (ISIT 2014) speculates that the MDS condition, which guarantees the existence of MDS matrices with a prescribed set of zeros over large fields, is in fact sufficient for existence of such matrices over small fields. We prove this conjecture.

In this paper two-dimensional convolutional codes with finite support are considered, i.e., convolutional codes whose codewords have compact support indexed in N and take values in F, where F is a finite field. The main goal of this work is to analyze the (free) distance properties of this type of codes of rate 1/n and degree δ. We first establish an upper bound on the maximum possible distance...

The Main Conjecture on maximum distance separable (MDS) codes states that, except for some special cases, the maximum length of a q-ary linear MDS code of is q+1. This conjecture does not hold true for near maximum distance separable codes because of the existence of q-ary near-MDS elliptic codes having length bigger than q+1. An interesting related question is whether a near-MDS elliptic code ...

Abstract. The paper deals with the diffusion approximation of the Boltzmann equation for semiconductors in the presence of spatially oscillating electrostatic potential. When the oscillation period is of the same order of magnitude as the mean free path, the asymptotics leads to the Drift-Diffusion equation with a homogenized electrostatic potential and a diffusion matrix involving the small sc...

We consider the problem of constructing exact-repair minimum storage regenerating (MSR) codes, for which both the systematic nodes and parity nodes can be repaired optimally. Although there exist several recent explicit high-rate MSR code constructions (usually with certain restrictions on the coding parameters), quite a few constructions in the literature only allow the optimal repair of syste...