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A new characterization of group action-based perfect nonlinearity

机译:基于群体行为的完全非线性的新表征

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摘要

The left-regular multiplication is explicitly embedded in the notion of perfect nonlinearity. But there exist many other group actions. By replacing translations by another group action the new concept of group action-based perfect nonlinearity has been introduced. In this paper we show that this generalized concept of nonlinearity is actually equivalent to a new bentness notion that deals with functions defined on a finite Abelian group G that acts on a finite set X and with values in the finite-dimensional vector space of complex-valued functions defined on X.
机译:左正则乘法被明确地嵌入到完美非线性的概念中。但是,还有许多其他的团体行动。通过用另一个小组动作代替翻译,引入了基于小组动作的完全非线性的新概念。在本文中,我们证明了这种非线性的广义概念实际上等效于一个新的弯曲概念,该概念处理在有限阿贝尔群G上定义的函数,该阿贝尔群G作用在有限集X上,并且具有复维的有限维向量空间中的值。 X上定义的有价值的函数。

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