Geodesic
The nonlinearity index for a~piecewise-linear substitution of the additive group of the field~$\mathbb F_{2^n}$
Prikladnaâ diskretnaâ matematika, no. 4 (2015), pp. 32-42

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In this paper, we give a lower bound on the nonlinearity of permutations on a field $\mathbb F_{2^n}$ with restrictions to cosets of $H$ in $\mathbb F_{2^n}^*$, $H\mathbb F_{2^n}^*$, $|H|=l$, $l\cdot r=2^n-1$, being the maps $x\mapsto A_jx$, $A_j\in\mathbb F_{2^n}^*$, $j=0,\dots,r-1$. Nonlinearity spectra of this permutations are found in the cases $r=3,5$.
Keywords: piecewise-linear function, permutation of a finite field, nonlinearity. 
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     author = {A. E. Trishin},
     title = {The nonlinearity index for a~piecewise-linear substitution of the additive group of the field~$\mathbb F_{2^n}$},
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A. E. Trishin. The nonlinearity index for a~piecewise-linear substitution of the additive group of the field~$\mathbb F_{2^n}$. Prikladnaâ diskretnaâ matematika, no. 4 (2015), pp. 32-42. http://geodesic.mathdoc.fr/item/PDM_2015_4_a2/