On Perfect Weighted Coverings with Small Radius

We extend the results of our previous paper [8] to the nonlinear case: The Lloyd polynomial of the covering has at least R distinct roots among 1, ... , n, where R is the covering radius. We investigate PWC with diameter 1, finding a partial characterization. We complete an investigation begun in [8] on linear PMC with distance 1 and diameter 2

Weighted Coverings and Packings

In this paper we introduce a generalization of the concepts of coverings and packings in Hamming space called weighted coverings and packings. This allows us to formulate a number of well-known coding theoretical problems in a uniform manner. We study the existence of perfect weighted codes, discuss connections between weighted coverings and packings, and present many constructions for them

Covering Radius 1985-1994

We survey important developments in the theory of covering radius during the period 1985-1994. We present lower bounds, constructions and upper bounds, the linear and nonlinear cases, density and asymptotic results, normality, specific classes of codes, covering radius and dual distance, tables, and open problems