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...

In this paper properties of cell matrices are studied. A determinant of such a matrix is given in a closed form. In the proof a general method for determining a determinant of a symbolic matrix with polynomial entries, based on multivariate polynomial Lagrange interpolation, is outlined. It is shown that a cell matrix of size n > 1 has exactly one positive eigenvalue. Using this result it is pr...

We evaluate the dual cone of set diagonally dominant matrices (resp., scaled matrices), namely $$\mathcal{DD}_n^*$$ $$\mathcal{SDD}_n^*$$ ), as an approximation semidefinite cone. prove that norm normalized distance, proposed by Blekherman et al. [5], between a $$\mathcal{S}$$ and has same value whenever $$\mathcal{SDD}_n^* \subseteq \mathcal{S} \mathcal{DD}_n^*$$ . This implies distance is not...

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 that all the lightest MDS matrices have only 10 XOR counts. Besides, all these lightest MDS matrices can be classified to 3 types, and some necessary and sufficient conditions are presented for them ...

Interconnected power system networks are multi loop structured. Settings determination of all over current and distance relays in such networks can be in different forms and complicated. The main problem is the determination of starting points i.e. the location of starting relays in the procedure for settings, which is referred to as break points. In this paper, a new approach based on graph th...

We present the combinatorial design for a kind of matrices called all-adjacent matrices. Such a matrix is constructed from a given set of elements; each element of the matrix is adjacent, within some column, to every other element of the set. We present the algorithm for constructing an all-adjacent matrix. These matrices have an important application—to the laying out of logical disks in a sha...

Regular boundary value problems on a distance-regular graph associated with Schrödinger operators are analyzed. These problems include the cases in which the boundary has one or two vertices. In each case, the Green matrices are given in terms of two families of orthogonal polynomials, one of them corresponding with the distance polynomials of the distance-regular graphs.

Regular boundary value problems on a distance-regular graph associated with Schrödinger operators are analyzed. These problems include the cases in which the boundary has one or two vertices. In each case, the Green matrices are given in terms of two families of orthogonal polynomials, one of them corresponding with the distance polynomials of the distance-regular graphs.

Many structural comparison methods of proteins have been proposed [2,3,4,5]. Among them, distance matrices, approximation of structure, and vector representation are the most commonly used. The distance matrices, also called distance plots or distance maps, contain all the pair-wise distances between alpha-carbon atoms, i.e. Cα atoms of each residue [3]. A matrix is a twodimensional (2D) repres...

We discuss the problem of recognizing permuted Van der Veen (VdV) matrices. It is well known that the TSP with a VdV matrix as distance matrix is pyramidally solvable. In this note we solve the problem of recognizing permuted strong VdV matrices. This yields an O(n4) time algorithm for the TSP with a permuted Euclidean VdV matrix. The problem, however, of recognizing permuted VdV matrices in ge...