Let n be any fixed positive integer. Every circulant weighing matrix of weight n arises from what we call an irreducible orthogonal family of weight n. We show that the number of irreducible orthogonal families of weight n is finite and thus obtain a finite algorithm for classifying all circulant weighing matrices of weight n. We also show that, for every odd prime power q, there are at most fi...

In this paper we obtain at least 61 new singly even (Type I) binary [72,36,12] self-dual codes as a quasi-cyclic codes with m=2 (tailbitting convolutional codes) and at least 13 new doubly even (Type II) binary [72,36,12] self-dual codes by replacing the first row in each circulant in a double circulant code by "all ones" and "all zeros" vectors respectively. Keywords—convolutional encoding, qu...

In this paper we obtain [60,30,12], [64,32,12], [68,34,12], [72,36,12] doubly even self-dual codes as tailbitting convolutional codes with the smallest constraint length K=9. In this construction one information bit is modulo two add to the one of the encoder outputs and this row will replace the first row in the double circulant matrix. The pure double circulant construction with K=10 is also ...

The distance energy of a graph G is a recently developed energy-type invariant, defined as the sum of absolute values of the eigenvalues of the distance matrix of G. There was a vast research for the pairs and families of non-cospectral graphs having equal distance energy, and most of these constructions were based on the join of graphs. A graph is called circulant if it is Cayley graph on the ...

In this paper, we propose a method to generalize Strang's circulant preconditioner for arbitrary n-by-n matrices An. The n 2 th column of our circulant preconditioner Sn is equal to the n 2 th column of the given matrix An. Thus if An is a square Toeplitz matrix, then Sn is just the Strang circulant preconditioner. When Sn is not Hermitian, our circulant preconditioner can be deened as (S n Sn)...

In this paper, we completely determine the connectivity of every infinite circulant digraphs and prove that almost all infinite circulant digraphs are infinitely strongly connected and therefore have both oneand two-way infinite Hamiltonian paths.

Circulant graphs are an extremely well-studied subclass of regular graphs, partially because they model many practical computer network topologies. It has long been known that the number of spanning trees in n-node circulant graphs with constant jumps satisfies a recurrence relation in n. For the non-constant-jump case, i.e., where some jump sizes can be functions of the graph size, only a few ...

a kernel $j$ of a digraph $d$ is an independent set of vertices of $d$ such that for every vertex $w,in,v(d),setminus,j$ there exists an arc from $w$ to a vertex in $j.$in this paper, among other results, a characterization of $2$-regular circulant digraph having a kernel is obtained. this characterization is a partial solution to the following problem: characterize circulant digraphs which hav...