In this work, we extend two extremal codes of length 64 which were obtained by the authors as bordered-double-circulant codes over R2. Using the extension, we have constructed seven new extremal binary codes of length 66 which were not previously known to exist.

This article concerns the system identification of a class of large scale systems called “circulant systems”. Circulant systems have a special property that allows them to be decomposed into simpler subsystems through a state transformation. This property has been used in literature for control design, and here we show how it can be used for system identification. The approach that is proposed ...

Quadratic residue codes have been one of the most important classes of algebraic codes. They have been generalized into duadic codes and quadratic double circulant codes. In this paper we introduce a new subclass of double circulant codes, called duadic double circulant codes, which is a generalization of quadratic double circulant codes for prime lengths. This class generates optimal self-dual...

In a graph G, a k-container Ck(u, v) is a set of k disjoint paths joining u and v. A k-container Ck(u, v) is k ∗-container if every vertex of G is passed by some path in Ck(u, v). A graph G is k ∗-connected if there exists a k∗-container between any two vertices. An m-regular graph G is super-connected if G is k∗-connected for any k with 1 k m. In this paper, we prove that the recursive circula...

Identifying and locating-dominating codes have been studied widely in circulant graphs of type Cn(1, 2, 3, . . . , r) over the recent years. In 2013, Ghebleh and Niepel studied locatingdominating and identifying codes in the circulant graphs Cn(1, d) for d = 3 and proposed as an open question the case of d > 3. In this paper we study identifying, locating-dominating and self-identifying codes i...

Given two k element subsets S,T ⊆ Zn, we give a quasi-linear algorithm to either find λ ∈ Z∗n such that S = λT or prove that no such λ exists. This question is closely related to isomorphism testing of circulant graphs and has recently been studied in the literature. © 2005 Elsevier B.V. All rights reserved.

In this paper we obtain a number of [70,35,12] singly even self-dual codes as a quasi-cyclic codes with m=2 (tailbitting convolutional codes). One of them is the first known code with parameters Beta=140 Gamma=0. All codes are not pure double circulant i.e. could not be represented in systematic form. Keywords—convolutional encoding, quasi-cyclic codes weight enumeratorg, double circulant

In this paper, we classify 2-closed (in Wielandt’s sense) permutation groups which contain a normal regular cyclic subgroup and prove that for each such group G, there exists a circulant Γ such that Aut(Γ) = G.