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Quadratic functions with prescribed spectra

Abstract : We study quadratic Boolean functions f from F2n to F2, which are well-known to have plateaued Fourier spectrum Fs;f , i.e., their Fourier coefficients are in the set {0,+_2(n+s)/2 } for some integer 0 ≤ s ≤ n-1. For various types of integers n, we determine possible values of s, construct f with Fs;f for a prescribed s, and present enumeration results in case n is a power of 2. Our work generalizes some of the earlier results of Khoo et. al. ([5]) on near-bent functions and provides a simple proof of a result of Fitzgerald ([2]) on degenerate quadratic forms.
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https://hal.inria.fr/inria-00614440
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Submitted on : Thursday, August 11, 2011 - 12:19:11 PM
Last modification on : Monday, February 11, 2019 - 5:32:02 PM
Long-term archiving on: : Monday, November 12, 2012 - 3:17:51 PM

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Wilfried Meidl, Alev Topuzoglu. Quadratic functions with prescribed spectra. WCC 2011 - Workshop on coding and cryptography, Apr 2011, Paris, France. pp.371-378. ⟨inria-00614440⟩

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