In this paper, we will employ the technique used in the proof of classical Singleton bound to derive upper bounds for rank metric codes and Ferrers diagram rank metric codes. These upper bounds yield the rank distance Singleton bound and an upper bound presented by Etzion and Silberstein respectively. Also we introduce generalized Ferrers diagram rank metric code which is a Ferrers diagram rank...

Let be a distance-regular graph with adjacency matrix A. Let I be the identity matrix and J the all-1 matrix. Let p be a prime. We study the p-rank of the matrices A + bJ − cI for integral b, c and the p-rank of corresponding matrices of graphs cospectral with . Using the minimal polynomial of A and the theory of Smith normal forms we first determine which p-ranks of A follow directly from the ...

It has been well known that the suitable criteria for Space time trellis codes (STTC) designed over slow Nakagami fading channel for product of rank and number of receiver antennas ) are maximization of minimum rank and maximize the minimum product of nonzero eigenvalues for rank and determinant criteria. But for large product i.e. for ), the design of codes with minimum error probability and m...

We present low-rank methods for event detection. We assume that normal observation come from a low-rank subspace, prior to being corrupted by a uniformly distributed noise. Correspondingly, we aim at recovering a representation of the subspace, and perform event detection by running point-to-subspace distance query in `∞, for each incoming observation. In particular, we use a variant of matrix ...

We use Lie-theoretic methods to explicitly compute the full spectrum of Laplace--Beltrami operator on homogeneous spheres which occur as geodesic distance in (compact or noncompact) symmetric spaces rank one, and provide a single unified formula for all cases. As an application, we find resonant radii compact case, i.e., where there is bifurcation embedded constant mean curvature spheres, show ...

We present a short overview of results obtained by a systematic survey of line radiation events observed by the DEMETER spacecraft at an altitude of 700 km. We find two different classes of events that can be easily distinguished by the observed frequency separation of lines forming the event – if it is 50/100 Hz or 60/120 Hz then the event is most probably caused by electromagnetic radiation f...

Recent research and applications for evaluation and quality estimation of Machine Translation require statistical measures for comparing machine-predicted ranking against gold sets annotated by humans. Additional to the existing practice of measuring segment-level correlation with Kendall tau, we propose using ranking metrics from the research field of Information Retrieval such as Mean Recipro...