On the distribution of Boolean function nonlinearity

Simon Litsyn*, Alexander Shpunt

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Nonlinearity is the number of bits which must change in the truth table of a Boolean function to reach the closest affine function. It may be expressed through the maximum of the absolute value of a component in the function's Walsh-Hadamard transform. Concentration of nonlinearity is proved. The derived bounds on the concentration point and tails of the distribution are tighter than the earlier known ones.

Original languageEnglish
Pages (from-to)79-95
Number of pages17
JournalSIAM Journal on Discrete Mathematics
Issue number1
StatePublished - 2008


  • Binomial sums
  • Boolean functions
  • Concentration of nonlinearity
  • Second moment method
  • Tails of binomial distribution
  • Walsh-Hadamard transform


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