Related papers: A Complete Characterization of Irreducible Cyclic …
Generalized bicycle (GB) codes is a class of quantum error-correcting codes constructed from a pair of binary circulant matrices. Unlike for other simple quantum code ans\"atze, unrestricted GB codes may have linear distance scaling. In…
In this paper, a unique form of generators of a constacyclic code of arbitrary length over a non-chain ring of the type $\mathtt{R_{_{\theta}}}=Z_{4}+\nu Z_{4}, \nu^{2}=\theta \in Z_{4}+\nu Z_{4}$ has been obtained. Further, rank and…
An easily computable dimension (or ECD) group code in the group algebra $\mathbb{F}_{q}G$ is an ideal of dimension less than or equal to $p=char(\mathbb{F}_{q})$ that is generated by an idempotent. This paper introduces an easily computable…
In this paper convolutional codes with cyclic structure will be investigated. These codes can be understood as left principal ideals in a suitable skew-polynomial ring. It has been shown in [3] that only certain combinations of the…
For a given graph whose edges are labeled with general real numbers, we consider the set of functions from the vertex set into the Euclidean plane such that the distance between the images of neighbouring vertices is equal to the…
In this paper, we introduce a new parameter of a code, referred to as the remoteness, which can be viewed as a dual to the covering radius. Indeed, the remoteness is the minimum radius needed for a single ball to cover all codewords. After…
Using closure concepts, we show that within every undirected network, or graph, there is a unique irreducible subgraph which we call its "spine". The chordless cycles which comprise this irreducible core effectively characterize the…
Cyclic codes are an important class of linear codes. Bounding the minimum distance of cyclic codes is a long-standing research topic in coding theory, and several well-known and basic results have been developed on this topic. Recently,…
In this paper, several families of irreducible constacyclic codes over finite fields and their duals are studied. The weight distributions of these irreducible constacyclic codes and the parameters of their duals are settled. Several…
We address the question of constructing explicitly quasi-uniform codes from groups. We determine the size of the codebook, the alphabet and the minimum distance as a function of the corresponding group, both for abelian and some nonabelian…
We give sufficient conditions for self-orthogonality with respect to symplectic, Euclidean and Hermitian inner products of a wide family of quasi-cyclic codes of index two. We provide lower bounds for the symplectic weight and the minimum…
We characterize the finite groups of minimal order that admit an irreducible complex character of degree $p$ or $p^2$, where $p$ is a prime.
A parametrization of irreducible unitary representations associated with the regular adjoint orbits of a hyperspecial compact subgroup of a reductive group over a non-dyadic non-archimedean local filed is presented. The parametrization is…
Linear quasi-cyclic product codes over finite fields are investigated. Given the generating set in the form of a reduced Gr{\"o}bner basis of a quasi-cyclic component code and the generator polynomial of a second cyclic component code, an…
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Inspired by the recent work on binary cyclic codes published in…
We show that the orbit closure of a directing module is regular in codimension one. In particular, this result gives information about a distinguished irreducible component of a module variety.
In this paper, we study cyclic codes over the ring $ \Z_p + u\Z_p +...+ u^{k-1}\Z_p $, where $u^k =0$. We find a set of generator for these codes. We also study the rank, the dual and the Hamming distance of these codes.
Given a subshift over an arbitrary alphabet, we construct a representation of the associated unital algebra. We describe a criteria for the faithfulness of this representation in terms of the existence of cycles with no exits. Subsequently,…
Cyclic codes are an important subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics. In this paper, two families of optimal ternary cyclic codes are presented. The first…
A unitary design is a collection of unitary matrices that approximate the entire unitary group, much like a spherical design approximates the entire unit sphere. In this paper, we use irreducible representations of the unitary group to find…