Some Aspects of Hankel Matrices in Coding Theory and Combinatorics

Hankel Matrices in Coding Theory and Combinatorics

On Fischer{frobenius Transformations and the Structure of Rectangular Block Hankel Matrices

In this paper, we develop three essential ingredients of an algebraic structure theory of nite block Hankel matrices. The development centers around a transformation of block Hankel matrices, rst introduced by Fischer and Frobenius for scalar Hankel matrices. We prove three results: First, Iohvidov's fundamental notion of the characteristic of a Hankel matrix is extended to the block matrix cas...

Generalized partial realizations

In this paper we extend Kalman's concept of partial realization and deene generalized partial realizations of nite matrix sequences by descriptor systems. Our deenition is in agreement with the realization theory for deterministic boundary value descriptor systems 15]. The aim of this contribution is to prove a counterpart of Kalman's main theorem of realization theory for generalized partial r...

On the computation of the nullspace of Toeplitz–like matrices

The knowledge of the nullspace and its size of some structured matrices, like Hankel and Toeplitz matrices, is important in many applications arising in system theory. In this paper we describe an algorithm to compute the kernel of Toeplitz and Hankel matrices based on the generalized Schur algorithm.

Wave propagation theory in offshore applications

A frequency-wavenumber-domain formulation is presented in this paper for calculation of the Green's functions and wave propagation modes in a stratified fluid body underlain by a layered viscoelastic soil medium. The Green's functions define the solid and fluid displacements and fluid pressures due to uniform disk loads acting in either the soil or fluid media. The solution is in the frequency ...