Multicovering Bounds from Linear Inequalities (Extended Abstract)

The multicovering radii of a code are natural generalizations of the covering radius in which the goal is to cover all m-tuples of vectors for some m as cheaply as possible. In this paper we use the method of linear inequalities to obtain new lower bounds on the sizes of codes achieving given multicovering radii. These bounds arise from linear inequalities involving the weight distributions of the code.