Algebraic techniques are employed to obtain necessary conditions for the existence of certain circulant weighing matrices. As an application we rule out the existence of many circulant weighing matrices. We study orders n = 8 +8+1, for 10 ~ 8 ~ 25. These orders correspond to the number of points in a projective plane of order 8.

We give a classification of all double circulant doubly even self-dual [72, 36, 12] codes. We also demonstrate that every double circulant doubly even self-dual [72, 36, 12] code has no extremal doubly even self-dual [72, 36, 16] neighbor.

We have extended our work in [1] and this paper investigates combinatorial properties of circulant networks including best containers, wide diameter, fault diameter and Rabin number. These properties have received much attention recently in the study of interconnection networks. In addition to these parameters we introduce fault wide diameter and study this parameter for circulant networks.

We introduce the smt toolbox for Matlab. It implements optimized storage and fast arithmetics for circulant and Toeplitz matrices, and is intended to be transparent to the user and easily extensible. It also provides a set of test matrices, computation of circulant preconditioners, and two fast algorithms for Toeplitz linear systems.

In this paper security aspects of the existing symmetric key encryption schemes based on Hadamard matrices are examined. Hadamard matrices itself have symmetries like one circulant core or two circulant core. Here, we are exploiting the inherent symmetries of Hadamard matrices and are able to perform attacks on these encryption schemes. It is found that entire key can be obtained by observing t...

We combine some basic techniques of linear algebra with some expressions for Toeplitz and circulant matrices and the properties of Gaussian random matrices to estimate the norms of Gaussian Toeplitz and circulant random matrices and their inverses. In the case of circulant matrices we obtain sharp probabilistic estimates, which show that the matrices are expected to be very well conditioned. Ou...

In this paper, we propose a new low-rank tensor model based on the circulant algebra, namely, twist tensor nuclear norm or t-TNN for short. The twist tensor denotes a 3-way tensor representation to laterally store 2D data slices in order. On one hand, t-TNN convexly relaxes the tensor multi-rank of the twist tensor in the Fourier domain, which allows an efficient computation using FFT. On the o...

An r × r matrix A = [aij] over a field F is called circulant if aij = a0, ( j−i) mod r . An [n = 2r, k = r] linear code over F = GF(q) is called double-circulant if it is generated by a matrix of the form [I A], where A is an r × r circulant matrix. In this work we first employ the Fourier transform technique to analyze and construct several families of double-circulant codes. The minimum dista...