let $cr_n(f_p)$ denote the algebra of $n times n$ circulant‎ ‎matrices over $f_p$‎, ‎the finite field of order $p$ a prime‎. ‎the‎ ‎order of the unit groups $mathcal{u}(cr_3(f_p))$‎, ‎$mathcal{u}(cr_4(f_p))$ and $mathcal{u}(cr_5(f_p))$ of algebras of‎ ‎circulant matrices over $f_p$ are computed‎.

Circulant matrices have attracted interest due to their rich algebraic structures and various applications. In this paper, the concept of vector-circulant matrices over finite fields is studied as a generalization of circulant matrices. The algebraic characterization for such matrices has been discussed. As applications, constructions of vector-circulant based additive codes over finite fields ...

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 paper‎, ‎some algebraic and geometrical properties of the rank$-k$ numerical hulls of normal matrices are investigated‎. ‎A characterization of normal matrices whose rank$-1$ numerical hulls are equal to their numerical range is given‎. ‎Moreover‎, ‎using the extreme points of the numerical range‎, ‎the higher rank numerical hulls of matrices of the form $A_1 oplus i A_2$‎, ‎where $A_1...

In this paper, it is considered a g-circulant, right circulant, left circulant and a special kind of tridiagonal matrices whose entries are h(x)-Fibonacci polynomials. The determinant of these matrices is established and with the tridiagonal matrices we show that the determinant is equal to the nth term of the h(x)-Fibonacci polynomials.

In order to efficiently compute some combinatorial designs based upon circulant matrices which have different, defined numbers of 1's and 0's in each row and column we need to find candidate vectors with differing weights and Hamming distances. This paper concentrates on how to efficiently create such circulant matrices. These circulant matrices have applications in signal processing, public ke...

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 paper circulant matrices in max-plus algebra are presented. Circulant matrices are special form of matrices which are entered by vector of inputs. For special types of matrices such as circulant matrices, the computation can often be performed in the simpler way than in the general case. The so-called max-plus algebra is useful for investigation of discrete events systems and the sequen...

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...