We consider an elliptic eigenvalue problem with a fast cellular flow of amplitude A, in a twodimensional domain with L cells. For fixed A, and L→∞, the problem homogenizes, and has been well studied. Also well studied is the limit when L is fixed, and A → ∞. In this case the solution equilibrates along stream lines. In this paper, we show that if both A → ∞ and L → ∞, then a transition between ...

Let L be a second-order partial differential operator in R e. Let R e be the finite union of disjoint polyhedra. Suppose that the diffusion matrix is everywhere non singular and constant on each polyhedron, and that the drift coefficient is bounded and measurable. We show that the martingale problem associated with L is well-posed.

The algebraic setting for threshold secret sharing scheme can vary, dependent on the application. This algebraic setting can limit the number of participants of an ideal secret sharing scheme. Thus it is important to know for which thresholds one could utilize an ideal threshold sharing scheme and for which thresholds one would have to use nonideal schemes. The implication is that more than one...

In this work, we study cyclic codes that have generators as Fibonacci polynomials over finite fields. We show that these cyclic codes in most cases produce families of maximum distance separable and optimal codes with interesting properties. We explore these relations and present some examples. Also, we present applications of these codes to secret sharing schemes. Mathematics Subject Classific...

Maximum distance separable (MDS) matrices have applications not only in coding theory but are also of great importance in the design of block ciphers and hash functions. It is highly nontrivial to find MDS matrices which could be used in lightweight cryptography. In a SAC 2004 paper, Junod et. al. constructed a new class of efficient MDS matrices whose submatrices were circulant matrices and th...

We study a recently proposed design approach of Feistel structure which employs diffusion matrices in a switching way. At ASIACRYPT 2004, Shirai and Preneel have proved that large numbers of S-boxes are guaranteed to be active if a diffusion matrix used in a round function is selected among multiple matrices. However the optimality of matrices required by the proofs sometimes pose restriction t...

We propose a cell-centred symmetric scheme which combines the advantages of MPFA (multi point flux approximation) schemes such as the L or the O scheme and of hybrid schemes: it may be used on general non conforming meshes, it yields a 9-point stencil on two-dimensional quadrangular meshes, it takes into account the heterogeneous diffusion matrix, and it is coercive and convergent. The scheme r...

We consider the caching of content in the mobile devices in a wireless network using maximum distance separable (MDS) codes. We focus on a small cell, served by a base station (BS), where mobile devices arrive and depart according to a Poisson birth-death process. Users requesting a particular file download coded symbols from caching devices using device-todevice communication. If additional sy...

Given an LCD group code C in a group algebra KG, we inspect kinship between C and G, more precisely between the subgroup structures of G and C. When C is MDS, the inter relation between K and G becomes more impressive. Application of Sylow theorem facilitated us to explore the inter relation between G and K (when C is LCD and MDS) in more general way and finally we get the result of Cruz and Wi...

Maximal distance separable (MDS) matrices are important components for block ciphers. In this paper, we present an algorithm for searching 4 × 4 MDS matrices over GL(4, F2). By this algorithm, we find all the lightest MDS matrices have only 10 XOR counts. Besides, all these lightest MDS matrices are classified to 3 types, and some necessary and sufficient conditions are presented for them as we...