1 Abstract In this paper we present a time-polynomial recognition algorithm for circulant graphs of prime order. A circulant graph G of order n is a Cayley graph over the cyclic group Z n : Equivalently, G is circulant ii its vertices can be ordered such that the corresponding adjacency matrix becomes a circulant matrix. To each circulant graph we may associate a coherent connguration A and, in...

In this paper, a recently introduced block circulant preconditioner for the linear systems of the codes for ordinary differential equations (ODEs) is investigated. Most ODE codes based on implicit formulas, at each integration step, need the solution of one or more unsymmetric linear systems that are often large and sparse. Here, the boundary value methods, a class of implicit methods for the n...

Properties and potential applications of the block pulse response circulant matrix (PRCM) and its singular value decomposition (SVD) are investigated in relation to MIMO control and identification. The SVD of the PRCM is found to provide complete directional as well as frequency decomposition of a MIMO system in a real matrix form. Three examples were considered: design of MIMO FIR controller, ...

This paper considers random (non-Hermitian) circulant matrices, and proves several results analogous to recent theorems on non-Hermitian random matrices with independent entries. In particular, the limiting spectral distribution of a random circulant matrix is shown to be complex normal, and bounds are given for the probability that a circulant sign matrix is singular.

Discrete body of revolution (DBOR) codes can accelerate moment method (MoM) solutions for scattering geometries possessing discrete circular symmetry. Traditional DBOR formulations require modifications to the incident field, such as decomposition into circular modes. While appropriate for methods employing direct solvers, approaches employing iterative solvers are disadvantaged by this dramati...

Maximum distance separable (MDS) matrices have applications not only in coding theory but are also of great importance in the design of block ciphers and hash functions. It is highly nontrivial to find MDS matrices which could be used in lightweight cryptography. In a SAC 2004 paper, Junod et. al. constructed a new class of efficient MDS matrices whose submatrices were circulant matrices and th...

We show that a simple geometric result suffices to derive the form of the optimal solution in a large class of finiteand infinite-dimensional maximum entropy problems concerning probability distributions, spectral densities, and covariance matrices. These include Burg’s spectral estimation method and Dempster’s covariance completion, as well as various recent generalizations of the above. We th...

A new method of obtaining a sequence isolated complex Hadamard matrices (CHM) for dimensions $N\geqslant 7$, based on block-circulant structures, is presented. We discuss, several analytic examples resulting from modification the Sinkhorn algorithm. In particular, we present orders $9$, $10$ and $11$, which elements are not roots unity, also multiparametric families order $10$. note novel conne...

We investigate the notion of cyclicity for convolutional codes as it has been introduced in the papers [15, 18]. Codes of this type are described as submodules of F[z]n with some additional generalized cyclic structure but also as specific left ideals in a skew polynomial ring. Extending a result of [15], we show in a purely algebraic setting that these ideals are always principal. This leads t...