Geodesic
Characterization of mappings by the nonisometricity property
Matematičeskie voprosy kriptografii, Tome 10 (2019), pp. 77-116.

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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. 
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B. A. Pogorelov; M. A. Pudovkina. Characterization of mappings by the nonisometricity property. Matematičeskie voprosy kriptografii, Tome 10 (2019), pp. 77-116. http://geodesic.mathdoc.fr/item/MVK_2019_10_a5/

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