Characterization of mappings by the nonisometricity property

For an integer-valued metric $\mu $ on a vector space over $GF(2)$ we introduce a new measure which characterize the non-coordination between $\mu$ and transformation $g$ of the space. It is called a nonisometric index of transformation $g$. In this paper we deal with metrics which are invariant under a translation group of the vector space over $GF(2)$. For different classes of transformations (including involutions and APN permutations) we find the values of nonisometric indices or their extremal estimates.