On subspaces of Kloosterman zeros and permutations of the form L_1(x^-1)+L_2(x)

03/31/2020

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by   Faruk Göloğlu, et al.

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Permutations of the form F=L_1(x^-1)+L_2(x) with linear functions L_1,L_2 are closely related to several interesting questions regarding CCZ-equivalence and EA-equivalence of the inverse function. In this paper, we show that F cannot be a permutation if the kernel of L_1 or L_2 is too large. A key step of the proof is a new result on the maximal size of a subspace of F_2^n that contains only Kloosterman zeros, i.e. a subspace V such that K_n(v)=0 for all v ∈ V where K_n(v) denotes the Kloosterman sum of v.