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- W4300196065 abstract "Zhou 2013 introduced modified planar functions to describe $(2^n,2^n,2^n,1)$ relative difference sets $R$ as a graph of a function on the finite field $F_{2^n}$, and pointed out that projections of $R$ are difference sets that can be described by negabent or bent$_4$ functions, which are Boolean functions given in multivariate form. Objective of this paper is to contribute to the understanding of these component functions of modified planar functions. We first completely describe a multivariate version of modified planar functions in terms of their bent$_4$ components. In the second part we characterize the component functions of (univariate) modified planar functions in terms of appropriate generalizations of the Walsh-Hadamard transform, with respect to which they have a flat spectrum. We hereby obtain a description of modified planar functions by their components which is similar to that of the classical planar functions in odd characteristic as a vectorial bent function." @default.
- W4300196065 created "2022-10-03" @default.
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- W4300196065 date "2016-11-12" @default.
- W4300196065 modified "2023-09-30" @default.
- W4300196065 title "Modified planar functions and their components" @default.
- W4300196065 doi "https://doi.org/10.48550/arxiv.1611.04031" @default.
- W4300196065 hasPublicationYear "2016" @default.
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