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Mat. Vopr. Kriptogr., 2019, Volume 10, Issue 4, Pages 77–116 (Mi mvk309)  

Characterization of mappings by the nonisometricity property

B. A. Pogorelova, M. A. Pudovkinab

a Academy of Cryptography of the Russian Federation, Moscow
b Bauman Moscow State Technical University, Moscow

Abstract: 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.

Key words: integral metric, involution, APN permutation, Hamming metric, affine transformations.

DOI: https://doi.org/10.4213/mvk309

Full text: PDF file (362 kB)
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UDC: 515.124+519.719.2
Received 18.IV.2018

Citation: B. A. Pogorelov, M. A. Pudovkina, “Characterization of mappings by the nonisometricity property”, Mat. Vopr. Kriptogr., 10:4 (2019), 77–116

Citation in format AMSBIB
\Bibitem{PogPud19}
\by B.~A.~Pogorelov, M.~A.~Pudovkina
\paper Characterization of mappings by the nonisometricity property
\jour Mat. Vopr. Kriptogr.
\yr 2019
\vol 10
\issue 4
\pages 77--116
\mathnet{http://mi.mathnet.ru/mvk309}
\crossref{https://doi.org/10.4213/mvk309}


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