Related papers: On the algebraic structure of quasi group codes

The main purpose of this paper is to describe some published results and outline corresponding approaches which when applied to automorphism groups of algebras or groups establish that these groups are linear or non-linear.

The paper presents a comprehensive study of group codes from non-abelian split metacyclic group algebras. We derive an explicit Wedderburn-like decomposition of finite split metacyclic group algebras over fields with characteristic coprime…

Quantum families of maps between quantum spaces are defined and studied. We prove that quantum semigroup (and sometimes quantum group) structures arise naturally on such objects out of more fundamental properties. As particular cases we…

We describe and present a new construction method for codes using encodings from group rings. They consist primarily of two types: zero-divisor and unit-derived codes. Previous codes from group rings focused on ideals; for example cyclic…

An important question in the study of quasi-perfect codes is whether such codes can be constructed for all possible lengths $n$. In this paper, we address this question for specific values of $n$. First, we investigate the existence of…

A quasi-tree is a geodesic metric space quasi-isometric to a tree. We give a general construction of many actions of groups on quasi-trees. The groups we can handle include non-elementary (relatively) hyperbolic groups, rank 1 CAT(0)…

A finite graph $\Gamma$ is called $G$-symmetric if $G$ is a group of automorphisms of $\Gamma$ which is transitive on the set of ordered pairs of adjacent vertices of $\Gamma$. We study a family of symmetric graphs, called the unitary…

We completely characterize possible indices of quasi-cyclic subcodes in a cyclic code for a very broad class of cyclic codes. We present enumeration results for quasi-cyclic subcodes of a fixed index and show that the problem of enumeration…

Dlab and Ringel showed that algebras being quasi-hereditary in all total orders for indices of primitive idempotents becomes hereditary. So, we are interested in for which orders a given quasi-hereditary algebra is again quasi-hereditary.…

In this paper, we study a special class of quasi-homomorphisms, i.e. quasi-retractions from a group to its subgroups. We first give some algebraic and geometric properties of quasi-retracts and then propose a theory of quasi-split short…

We introduce the notion of a quasi-connected reductive group over an arbitrary field to be an almost direct product of a connected semisimple group and a quasi-torus (a smooth group of multiplicative type). We show that a linear algebraic…

In 2019, Aterias et al. constructed pairs of quantum isomorphic, non-isomorphic graphs from linear constraint systems. This article deals with quantum automorphisms and quantum isomorphisms of colored versions of those graphs. We show that…

The algebraic structure on the subspace of the quasi-primary vectors given by the projection of the (n) products of a conformal superalgebra is formulated. As an application the complete list of simple physical conformal superalgebras is…

Quasi-twisted (QT) codes are a generalization of quasi-cyclic (QC) codes. Based on consta-cyclic simplex codes, a new explicit construction of a family of 2-generator quasi-twisted (QT) two-weight codes is presented. It is also shown that…

We study the quasi-isometric rigidity of a large family of finitely generated groups that split as graphs of groups with virtually free vertex groups and two-ended edge groups. Let $G$ be a group that is one-ended, hyperbolic relative to…

Based on cyclic and consta-cyclic simplex codes, a new explicit construction of a family of two-weight codes is presented. These two-weight codes obtained are in the form of 2-generator quasi-cyclic, or quasi-twisted structure. Based on…

We determine a condition on the minimum Hamming weight of some special abelian group codes and, as a consequence of this result, we establish that any such code is, up to permutational equivalence, a subspace of the direct sum of $s$ copies…

Using the technique of quasi difference sets we characterize geometry and automorphisms of configurations which can be presented as a join of some others, in particular - which can be presented as series of cyclically inscribed copies of…

In this paper we study quasi-symmetric conjugations of $C^2$ weakly order-preserving circle maps with a flat interval. Under the assumption that the maps have the same rotation number of bounded type and that bounded geometry holds we…

We study automorphisms and representations of quasi polynomial algebras (QPAs) and quasi Laurent polynomial algebras (QLPAs). For any QLPA defined by an arbitrary skew symmetric integral matrix, we explicitly describe its automorphism…