An n × n matrix D = d[i, j] is said to be circulant, if the entries d[i, j] verifying (j − i) = k mod n, for some k, have the same value (for a survey on circulant matrix properties, see Davis (1979)). A directed (respectively, undirected) graph is circulant, if its adjacency matrix is circulant (respectively, symmetric, and circulant). Similarly, a weighted graph is circulant, if its weighted ...

In this article, we analyze the circulant structure of generalized circulant matrices to reduce the search space for finding lightweight MDS matrices. We first show that the implementation of circulant matrices can be serialized and can achieve similar area requirement and clock cycle performance as a serial-based implementation. By proving many new properties and equivalence classes for circul...

We first give the style spectral decomposition of a special skew circulant matrix C and then get the style decomposition of arbitrary skew circulant matrix by making use of the Kronecker products between the elements of first row in skew circulant and the special skew circulant C. Besides that, we obtain the singular value of skew circulant matrix as well. Finally, we deal with the optimal back...

Circulant matrices can be effective preconditioners for linear systems of equations with a Toeplitz matrix. Several approaches to construct such preconditioners have been described in the literature. This paper focuses on the superoptimal circulant preconditioners proposed by Tyrtyshnikov, and investigates a generalization obtained by allowing generalized circulant matrices. Numerical examples ...

In this article, we analyze the circulant structure of generalized circulant matrices to reduce the search space for finding lightweight MDS matrices. We first show that the implementation of circulant matrices can be serialized and can achieve similar area requirement and clock cycle performance as a serial-based implementation. By proving many new properties and equivalence classes for circul...

Anti-circulant tensors have applications in exponential data fitting. They are special Hankel tensors. In this paper, we extend the definition of anti-circulant tensors to generalized anticirculant tensors by introducing a circulant index r such that the entries of the generating vector of a Hankel tensor are circulant with module r. In the special case when r=n, where n is the dimension of the...

A formula for the distance of a Toeplitz matrix to the subspace of {e}-circulant matrices is presented, and applications of {e}-circulant matrices to preconditioning of linear systems of equations with a Toeplitz matrix are discussed. Copyright c © 2006 John Wiley & Sons, Ltd. key words: Toeplitz matrix, circulant matrix, {e}-circulant, matrix nearness problem, distance to normality, preconditi...

In this study, the authors propose new methods using a divide-and-conquer strategy to generate n × n binary matrices (for composite n) with a high/maximum branch number and the same Hamming weight in each row and column. They introduce new types of binary matrices: namely, (BHwC)t, m and (BCwC)q, m types, which are a combination of Hadamard and circulant matrices, and the recursive use of circu...

Let F = (Kn,P) be a circulant homogeneous factorisation of index k, that means P is a partition of the arc set of the complete digraph Kn into k circulant factor digraphs such that there exists σ ∈ Sn permuting the factor circulants transitively amongst themselves. Suppose further such an element σ normalises the cyclic regular automorphism group of these circulant factor digraphs, we say F is ...