In this paper, we study self-dual codes over GF(p) where p = 11, 13, 17, 19, 23 and 29. A classification of such codes for small lengths is given. The largest minimum weights of these codes are investigated. Many maximum distance separable self-dual codes are constructed.

The purpose of this paper is to attain some optimality conditions for the identification of a diffusion matrix (material) under several restrictions. Assuming that the set of such diffusion matrices is closed for the H-convergence, we give a method to obtain admissible directions which applies to a not-necessarily convex control set. Our results permit obtaining the diffusion matrix from the st...

Ghulam Murtaza, Nassar Ikram 1,2 National University of Sciences and Technology, Pakistan [email protected] [email protected] Abstract. An MDS matrix is an important building block adopted by different algorithms that provides diffusion and therefore, has been an area of active research. In this paper, we present an idea of direct exponent and direct square of a matrix. We prove...

Diffusion layers are critical components of symmetric ciphers. MDS matrices are diffusion layers of maximal branch number which have been used in various symmetric ciphers. In this article, we examine decomposition of cyclic matrices from mathematical viewpoint and based on that, we present new cyclic MDS matrices. From the aspect of implementation, the proposed matrices have lower implementati...

In this paper we consider the fundamental question of optimizing finite field multiplications with one fixed element. Surprisingly, this question did not receive much attention previously. We investigate which field representation, that is which choice of basis, allows for an optimal implementation. Here, the efficiency of the multiplication is measured in terms of the number of XOR operations ...

Algebraic systems are constructed from which series of maximum distance separable (mds) codes are derived. The methods use unit and idempotent schemes.

In this work, we propose MDS-Tree and MDS-Matrix as novel high dimensional data visualization methods to gain insight in both the data aspect and dimension aspect of the data. Dimension metrics of the high dimensional dataset are first computed to create a hierarchy. In an MDS-Tree, each node is an MDS projection of the original data items on a specific subset of dimensions associated with the ...

Group classification of the generalized complex Ginzburg-Landau equations is presented. An approach to group classification of systems of reaction-diffusion equations with general diffusion matrix is developed.

The disk allocation problem addresses the issue of how to distribute a file on to several disks to maximize the concurrent disk accesses in response to a partial match query. In the past this problem has been studied for binary as well as for p-ary cartesian product files. In this paper, we propose a disk allocation strategy for non-uniform cartesian product files by a coding theoretic approach...

We present some results on almost maximum distance separable (AMDS) codes and Griesmer codes of dimension 4 over F5. We prove that no AMDS code of length 13 and minimum distance 5 exists, and we give a classification of some AMDS codes. Moreover, we classify the projective strongly optimal Griesmer codes over F5 of dimension 4 for some values of the minimum distance.