In the present work, the class of metrics connected with subsets of the linear space on the field, GF(2), is considered and a number of facts are established, which allow us to express the correcting capacity of codes for the additive channel in terms of this metrics. It is also considered a partition of the metric space, Bⁿ, by means of D-representable codes. The equivalence of D-representable and the perfect codes in the additive channel is proved.