New upper bounds on the covering radius of codes with known dual distance

Using the linear programming approach and the concept of weighted coverings we derive new upper bounds on the covering radius of codes with a given cardinality and a given dual distance. There has been a recent revival of interest in the problem of finding upper bounds on the covering radius of a code as a function of its size, dual distance or minimal distance. This problem relates to some methods of coding for write-once memories, interconnection networks, quantization, etc. If we assume that the minimal distance of a linear code is greater than 3 then the problem corresponds to evaluating the diameter of a subclass of Cayley graphs over Z₂^r of given degree and robustness