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Maximally nonlinear functions over finite fields

  • Vladimir G. Ryabov EMAIL logo
Published/Copyright: February 24, 2023

Abstract

An n-place function over a field Fq with q elements is called maximally nonlinear if it has the largest nonlinearity among all q-valued n-place functions. We show that, for even n=2, a function is maximally nonlinear if and only if its nonlinearity is qn1(q1)qn21 ; for n=1, the corresponding criterion for maximal nonlinearity is q − 2. For q>2 and even n=2, we describe the set of all maximally nonlinear quadratic functions and find its cardinality. In this case, all maximally nonlinear quadratic functions are quadratic bent functions and their number is smaller than the halved number of the bent functions.


NP “GST”

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Received: 2020-12-22
Published Online: 2023-02-24
Published in Print: 2023-02-23

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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