We give an explicit construction of circulant graphs of very high energy. This construction is based on Gauss sums. We also show the Littlewood conjecture can be used to establish new result for a certain class of circulant graphs. © 2005 Elsevier Inc. All rights reserved. AMS classification: 05C35; 05C50; 11T24; 42A05

We employ theoretical and computational techniques to construct new weighing matrices constructed from two circulants. In particular, we construct W (148, 144), W (152, 144), W (156, 144) which are listed as open in the second edition of the Handbook of Combinatorial Designs. We also fill a missing entry in Strassler’s table with answer ”YES”, by constructing a circulant weighing matrix of orde...

In this paper, we consider a g-circulant matrixA 1(T), whose the first row entries are generalized Tribonacci numbers T(a)i. We give an explicit formula of spectral norm matrix. When g = 1, also present upper and lower bounds for spread 1-circulant matrix A1(T).

We present a circulant and skew-circulant splitting (CSCS) iterative method for solving large sparse continuous Sylvester equations AX+XB=C, where the coefficient matrices A B are Toeplitz matrices. theoretical study shows that if factors of positive semi-definite (not necessarily Hermitian), at least one factor is definite, then CSCS converges to unique solution equation. In addition, our anal...

in this paper we consider the group algebra $r(c_2times‎ ‎d_infty)$‎. ‎it is shown that $r(c_2times d_infty)$ can be‎ ‎represented by a $4times 4$ block circulant matrix‎. ‎it is also‎ ‎shown that $mathcal{u}(mathbb{z}_2(c_2times d_infty))$ is‎ ‎infinitely generated‎.

let $cr_{n}(f)$ denote the algebra of $n times n$ circulant matrices over the field $f$. in this paper, we study the unit group of $cr_{n}(f_{p^m})$, where $f_{p^m}$ denotes the galois field of order $p^{m}$, $p$ prime.

In this work, we give three new techniques for constructing Hermitian self-dual codes over commutative Frobenius rings with a non-trivial involutory automorphism using $$\lambda$$ -circulant matrices. The constructions are derived as modifications of various well-known circulant codes. Applying these together the building-up construction, construct many best known quaternary lengths 26, 32, 36,...