Munuera, C., On MDS elliptic codes, Discrete Mathematics 117 (1993) 2799286. In this paper we give a bound for MDS (maximum distance separable) algebraic-geometric codes arising from elliptic curves. Several consequences are presented.

The lattice gas model in equilibrium is considered. We give a lower bound of the density-density time correlation for large time, which involves the bulk diffusion matrix in a physically natural way.

Due to their remarkable application in many branches of applied mathematics such as combinatorics, coding theory, and cryptography, Vandermonde matrices have received a great amount of attention. Maximum distance separable (MDS) codes introduce MDS matrices which not only have applications in coding theory but also are of great importance in the design of block ciphers. Lacan and Fimes introduc...

In the present paper, we investigate the problem of constructing MDS matrices with as few bit XOR operations as possible. The key contribution of the present paper is constructing MDS matrices with entries in the set of m ×m non-singular matrices over F2 directly, and the linear transformations we used to construct MDS matrices are not assumed pairwise commutative. With this method, it is shown...

In present paper, we investigate 4 problems. Firstly, it is known that, a matrix is MDS if and only if all sub-matrices of this matrix of degree from 1 to n are full rank. In this paper, we propose a theorem that an orthogonal matrix is MDS if and only if all sub-matrices of this orthogonal matrix of degree from 1 to bn2 c are full rank. With this theorem, calculation of constructing orthogonal...

Multidimensional scaling (MDS) is a collection of data analytic techniques for constructing conngura-tions of points from dissimilarity information about interpoint distances. A popular measure of the t of the constructed distances to the observed dissimilar-ities is the stress criterion, which must be minimized by numerical optimization. Empirical evidence concerning the existence of nonglobal...

The role of mesenchymal stromal cells (MSCs) in the pathogenesis of myelodysplastic syndromes (MDS) has been increasingly addressed, but has yet to be clearly elucidated. In this investigation, we found that MDS cells proliferated to a greater extent on MDS-derived MSCs compared to normal MSCs. Matrix metalloproteinase 1(MMP1), which was downregulated in MDS-MSCs, was identified as an inhibitor...

AES Rijndael is a block cipher developed by NIST as the Advanced Encryption Standard (AES) replacing DES and published as FIPS 197 in November 2001 [5] to address the threatened key size of Data Encryption Standard (DES). AES-Rijndael was developed by Joan Daemen and Vincent Rijmen, Rijndael [4, 5] and was selected from five finalists. Advancement in computation speed every day puts lots of pre...

Muscular dystrophies (MDs) are a heterogeneous group of diseases, caused by mutations in different components of sarcolemma, extracellular matrix, or enzymes. Inflammation and innate or adaptive immune response activation are prominent features of MDs. Various therapies under development are directed toward rescuing the dystrophic muscle damage using gene transfer or cell therapy. Here we discu...

MDS matrices allow to build optimal linear diffusion layers in block ciphers. However, MDS matrices cannot be sparse and usually have a large description, inducing costly software/hardware implementations. Recursive MDS matrices allow to solve this problem by focusing on MDS matrices that can be computed as a power of a simple companion matrix, thus having a compact description suitable even fo...