Coverings of the smallest Paige loop

A New Decoding Algorithm for Complete Decoding of Linear Block Codes

In this paper we present and describe an improved version of the Zero-Neighbors algorithm, which we call the Zero-Coverings algorithm. We also present a method for finding a smallest subset of codewords ( Zero-Coverings) which need to be stored to perform the Zero-Coverings algorithm. For some short codes, the sizes of Zero-Coverings are obtained by computer searches; for long codes, an asympto...

Connected coverings and an application to oriented matroids

In this paper we are interested in the following question: what is the smallest number of circuits, s(n,r), that is sufficient to determine every uniform oriented matroid of rank r on n elements? We shall give different upper bounds for s(n,r) by using special coverings called connected coverings. (~) 1998 Elsevier Science B.V. All rights reserved

ALGEBRAS WITH CYCLE-FINITE STRONGLY SIMPLY CONNECTED GALOIS COVERINGS

Let $A$ be a nite dimensional $k-$algebra and $R$ be a locally bounded category such that $R rightarrow R/G = A$ is a Galois covering dened by the action of a torsion-free group of automorphisms of $R$. Following [30], we provide criteria on the convex subcategories of a strongly simply connected category R in order to be a cycle- nite category and describe the module category of $A$. We p...

Finite Groups with p-Sylow Coverings

Multiple coverings of the farthest-off points and multiple saturating sets in projective spaces

For the kind of coverings codes called multiple coverings of the farthestoff points (MCF) we define μ-density as a characteristic of quality. A concept of multiple saturating sets ((ρ, μ)-saturating sets) in projective spaces PG(N, q) is introduced. A fundamental relationship of these sets with MCF codes is showed. Lower and upper bounds for the smallest possible cardinality of (1, μ)-saturatin...