A new approach to the covering radius of codes

We introduce a new approach which facilitates the calculation of the covering radius of a binary linear code. It is based on determining the normalized covering radius p. For codes of fixed dimension we give upper and lower bounds on p that arc reasonably close. As an application, an explicit formula is given for the covering radius of an arbitrary code of dimension <4. This approach also sheds light on whether or not a code is normal. All codes of dimension < 4 are shown to be normal, and an upper bound is given for the norm of an arbitrary code. This approach also leads to an amusing generalization of the BerlekampGale switching game.