Showing papers on "Circulant matrix published in 1975"

Some results on weighing matrices

Abstract: It is shown that if q is a prime power then there exists a circulant weighing matrix of order q2 + q + 1 with q2 nonzero elements per row and column.This result allows the bound N to be lowered in the theorem of Geramita and Wallis that “given a square integer k there exists an integer N dependent on k such that weighing matrices of weight k and order n and orthogonal designs (1, k) of order 2n exist for every n > N”.

(v, k, λ) Configurations and self-dual codes

Abstract: The incidence matrix of a (v, k, λ) configuration is used to construct a (2v, v) and a (2v + 2, v + 1) self-dual code. If the incidence matrix is a circulant, the codes obtained are quasi-cyclic and extended quasi-cyclic, respectively. The weight distributions of some codes of this type are obtained.

On the reduction of matrix functions

Abstract: Straightforward reduction of matrix functions without explicit use of the Lagrange-Sylvester (LS) theorem and of the characteristic roots is achieved by expansions in terms of Lucas polynomials. Use of the LS theorem within the framework of the Lucas polynomial method and, furthermore, of circulant matrices leads to substantial simplifications.