A class of APcN power functions over finite fields of even characteristic

07/14/2021

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by   Ziran Tu, et al.

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In this paper, we investigate the power functions F(x)=x^d over the finite field 𝔽_2^4n, where n is a positive integer and d=2^3n+2^2n+2^n-1. It is proved that F(x)=x^d is APcN at certain c's in 𝔽_2^4n, and it is the second class of APcN power functions over finite fields of even characteristic. Further, the c-differential spectrum of these power functions is also determined.