Asymptotically optimal Boolean functions
نویسندگان
چکیده
منابع مشابه
Asymptotically optimal Boolean functions
The largest Hamming distance between a Boolean function in $n$ variables and the set of all affine Boolean functions in $n$ variables is known as the covering radius $\rho_n$ of the $[2^n,n+1]$ Reed-Muller code. This number determines how well Boolean functions can be approximated by linear Boolean functions. We prove that \[ \lim_{n\to\infty}2^{n/2}-\rho_n/2^{n/2-1}=1, \] which resolves a conj...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2019
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2018.12.005