Showing papers on "Circulant matrix published in 1978"
TL;DR: C over GF(4) which have even weights and have the same weight distribution as the dual code C⊥ are studied, and an upper bound obtained on the minimum distance is obtained.
172 citations
TL;DR: Properties and definitions of Toeplitz and related matrices scattered throughout the literature are collected together, and presented in a unified form.
Abstract: Properties and definitions of Toeplitz and related matrices scattered throughout the literature are collected together, and presented in a unified form. Toeplitz, ortho-symmetric, Hankel, persymmetric, circulant and centrosymmetric matrices are covered. Inversion algorithms for general, special and block Toeplitz matrices are outlined. A considerable number of references is given
35 citations
TL;DR: This work presents a means of constructing this group of orthogonal matrices given the complete factorization of the minimal polynomial of T over F and gives an explicit formula for the number of n × n Orthogonal circulant matrices over GF(pl) and a similar formula for symmetric circulants.
8 citations
TL;DR: In this article, the Moore-Penrose inverse of such a "retrocirculant" was determined and the nonzero eigenvalues of the inverse were the reciprocals of the non zero eigen values of the retrocirculant.
7 citations
01 Jan 1978
TL;DR: The weight distributions of the (14, 7) and two inequivalent (26, 13)-codes arising from the incidence matrices of projective planes of orders 2 and 3 are determined.
Abstract: Some properties of a new class of codes constructed using circulant matrices over GF(3) will be discussed. In particular we determine the weight distributions of the (14, 7) and two inequivalent (26, 13)-codes arising from the incidence matrices of projective planes of orders 2 and 3.
5 citations
01 Jan 1978
TL;DR: For a given vector A := (a0,a1,...,an−1) in ℝn, simple necessary and sufficient conditions on a 0,a 1,a 2,an − 1 are established for the determinant of the circulant matrix of A to be positive, or negative, or zero as discussed by the authors.
Abstract: For a given vector A := (a0,a1,...,an−1) in ℝn, simple necessary and sufficient conditions on a0,a1,...,an−1 are established for the determinant of the circulant matrix of A to be positive, or negative, or zero. There is a striking difference between the conditions for n odd and the conditions for n even. The determinant of the skew-circulant matrix of A is similarly discussed.
3 citations
01 Apr 1978
TL;DR: A technique is described to approximate a linear time-invariant system by a linear m-adic invariant (LMI) system or, equivalently, approximate a circulant matrix by a supercircular matrix, which reduces the number of multiplies required for computing cyclic convolution.
Abstract: A technique is described to approximate a linear time-invariant (LTI) system by a linear m-adic invariant (LMI) system or, equivalently, approximate a circulant matrix by a supercirculant matrix. This approximation reduces the number of multiplies required for computing cyclic convolution. Furtermore, the concepts of LMI systems are presented in a tutorial fashion. Examples are included to illustrate the efficacy of the approximation technique.
1 citations
TL;DR: In this article, the influence of perturbative interaction on an exact point mass system, which is intrinsically degenerate, is studied using an action-angle formulation, and a specific application of interest is presented.
Abstract: Point mass systems in which the interaction matrix is a symmetric circulant occur in a wide variety of physical situations. In many cases also the interaction matrix, while not being a circulant, may differ only slightly from one. The dynamics of both exact and near-circulant systems are analysed in the present paper. In particular the influence of a perturbative interaction on an exact system, which is intrinsically degenerate, is studied using an action-angle formulation. A specific application of interest is presented.
1 citations