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Polynomials With Linear Structure and Maiorana–McFarland Construction

机译:线性结构多项式和Maiorana–McFarland构造

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摘要

In this paper, we study permutation polynomials over the finite fields that have linear structures. We present some results on such a permutation which transforms a hyperplane to another hyperplane. We fully characterize the bilinear polynomial with linear structure. The most important result of this paper is to show the relation between a Maiorana–McFarland function with an affine derivative and a polynomial with a linear structure. Moreover, we highlight this result in the context of resilient functions which are based on Maiorana–McFarland construction.
机译:在本文中,我们研究具有线性结构的有限域上的置换多项式。我们提出了关于将超平面转换为另一超平面的这种排列的一些结果。我们充分表征具有线性结构的双线性多项式。本文最重要的结果是显示具有仿射导数的Maiorana–McFarland函数与具有线性结构的多项式之间的关系。此外,我们在基于Maiorana–McFarland构建的弹性功能的上下文中强调了此结果。

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