科研之友
微信
新浪微博
Facebook
分享链接
摘要
The r-th order nonlinearity of a Boolean function is the minimum number of elements that have to be changed in its truth table to arrive at a Boolean function of degree at most r. It is shown that the (suitably normalised) r-th order nonlinearity of a random Boolean function converges strongly for all r >= 1. This extends results by Rodier for r = 1 and by Dib for r = 2. The methods in the present paper are mostly of elementary combinatorial nature and also lead to simpler proofs in the cases that r = 1 or 2.
- 出版日期2016-10
