Multidimensional $p$-adic metric and genetic code

We discuss the family of metrics in multimensional $p$-adic spaces. For a metric under consideration the set of balls differs from the set of balls for the standard multidimensional metric. Moreover, we it is possible to consider the metrics for which the form of the sets of balls depends on the scale and position. As the example of the introduced metric spaces we study the $2$-adic parametrization of the genetic code. We show that the degeneracy of the genetic code is described by the metric space from the considered family, i.e. the map of the genetic code is constant for the balls with respect to the metric from the introduced class.