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A Lower Bound on the Number of Boolean Functions with Median Correlation Immunity

Information Theory 2023-03-30 v1 math.IT
Authors: Vladimir N. Potapov
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Abstract

The number of nn-ary balanced correlation immune (resilient) Boolean functions of order n2\frac{n}{2} is not less than n2(n/2)−2(1+o(1))n^{2^{(n/2)-2}(1+o(1))} as n→∞n\rightarrow\infty. Keywords: resilient function, correlation immune function, orthogonal array

Keywords

resilient function correlation immune function orthogonal array boolean function lower bound

Cite

@article{arxiv.1910.02621,
  title  = {A Lower Bound on the Number of Boolean Functions with Median Correlation Immunity},
  author = {Vladimir N. Potapov},
  journal= {arXiv preprint arXiv:1910.02621},
  year   = {2023}
}

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