  In this paper, we introduce a new parameter of a code, referred to as the
remoteness, which can be viewed as a dual to the covering radius. Indeed, the
remoteness is the minimum radius needed for a single ball to cover all
codewords. After giving some general results about the remoteness, we then
focus on the remoteness of permutation codes. We first derive upper and lower
bounds on the minimum cardinality of a code with a given remoteness. We then
study the remoteness of permutation groups. We show that the remoteness of
transitive groups can only take two values, and we determine the remoteness of
transitive groups of odd order. We finally show that the problem of determining
the remoteness of a given transitive group is equivalent to determining the
stability number of a related graph.
