On the covering radius of codes

The covering radius of a code is the maximal distance of any vector from the code. This work gives a number of new results concerning , the minimal covering radius of any binary code of length and dimension . For example and are determined exactly, and reasonably tight bounds on are obtained for any when is large. These results are found by using several new constructions for codes with small covering radius. One construction, the amalgamated direct sum, involves a quantity called the norm of a code. Codes with norm are called normal, and may be combined efficiently. The paper concludes with a table giving bounds on for .