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- W2212615093 abstract "Theory of Boolean functions is a wide area of research in cryptography, coding theory, and combinatorics. One of the main criteria, with which a Boolean function is analyzed is its nonlinearity, that is its minimum distance to affine functions and the main tool to study nonlinearity of Boolean functions is the Walsh transform. There are various open problems regarding the construction and enumeration of Boolean functions with predetermined features such as nonlinearity (e.g. finding the number of Boolean functions with desired nonlinearity). Our study demonstrates partial results in finding a solution for some of these open problems such as the problem of determining a Boolean function once given the number $s = {a in GF(2)^n |  W_{f}(a)=0 }$. Moreover, we investigate the exact number of functions in $B_n$ containing a Walsh coefficient $|W_{f}(a)|$ for all $2^{n-1} leq |W_{f}(a)| leq 2^n$ and for some $|W_{f}(a)| leq 2^{n-1}$, in terms of $n$." @default.
- W2212615093 created "2016-06-24" @default.
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- W2212615093 date "2012-06-06" @default.
- W2212615093 modified "2023-09-23" @default.
- W2212615093 title "Counting Boolean Functions with Specified Values in their Walsh Spectrum" @default.
- W2212615093 hasPublicationYear "2012" @default.
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