A new family of error-correcting codes, called Fourier codes, is introduced. The code parity-check matrix, dimension and an upper bound on its minimum distance are obtained from the eigenstructure of the Fourier number theoretic transform. A decoding technique for such codes is proposed. Index Terms – finite field Fourier transform, number theoretic transform, eigensequences, linear block codes.

In this note, we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique. Our results are similar to some inequalities shown by Bhatia and Kittaneh in [Linear Algebra Appl. 308 (2000) 203-211] and [Linear Algebra Appl. 428 (2008) 2177-2191].

We demonstrate that the technique for calculating length of two-block matrix algebras, developed by author earlier, can be used to calculate lengths group algebras Abelian groups. find algebra a noncyclic order 2p2, where p > 2 is prime number, over field characteristic p, namely, we prove this equal 3p−2.

This research investigates the implementation mechanism of block-wise ILU(k) preconditioner on GPU. The block-wise ILU(k) algorithm requires both the level k and the block size to be designed as variables. A decoupled ILU(k) algorithm consists of a symbolic phase and a factorization phase. In the symbolic phase, a ILU(k) nonzero pattern is established from the point-wise structure extracted fro...

Run-time support for the CYCLIC(k) redistribution on the SPMD computation model is presently very relevant for the scientific community. This work is focused to the characterization of the sparse matrix redistribution and its associate problematic due to the use of compressed representations. Two main improvements about the buffering and the coordinates calculation modify the original algorithm...

A set of new formulae for the inverse of a block Hankel (or block Toeplitz) matrix is given. The formulae are expressed in terms of certain matrix Pad6 forms, which approximate a matrix power series associated with the block Hankel matrix. By using Frobenius-type identities between certain matrix Pad6 forms, the inversion formulae are shown to generalize the formulae of Gohberg-Heinig and, in t...

In this paper, a so-called auxiliary matrix polynomial Xn(z) and a true right formal orthogonal matrix polynomial (FOMP) A 1 n (z) is connected to each well-conditioned leading principal block submatrix of a given block Toeplitz matrix. From these two matrix polynomi-als, all other right FOMPs of block n of a system of block biorthogonal matrix polynomials with respect to the block Toeplitz mom...

Block coherence of matrices plays an important role in analyzing the performance of block compressed sensing recovery algorithms (Bajwa and Mixon, 2012). In this paper, we characterize two block coherence metrics: worstcase and average block coherence. First, we present lower bounds on worst-case block coherence, in both the general case and also when the matrix is constrained to be a union of ...