On the covering radius problem for codes: (II) Codes of low dimension; Normal and abnormal codes.

In this two-part paper we introduce the notion of a stable code, determine the maximal covering radius of any [n,k] code, and obtain a new upper bound on the normalized covering radius. We show that, for fixed k and large n, the minimal covering radius [n,k] is realized by a normal code in which all but one of the columns have multiplicity 1. Thus t[n+2,k] = t (n,k] + 1 for sufficiently large n. We also show that codes with n