A comparison of Carlet's second-order nonlinearity bounds

Sihem Mesnager, Gavin McGrew, James Davis, Dayton Steele, Katherine Marsten

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Carlet provides two bounds on the second-order nonlinearity of Boolean functions. We construct a family of Boolean functions where the first bound (the presumed weaker bound) is tight and the second bound is strictly worse than the first bound. We show that the difference between the two bounds can be made arbitrarily large.

Original languageEnglish (US)
Pages (from-to)427-436
Number of pages10
JournalInternational Journal of Computer Mathematics
Volume94
Issue number3
DOIs
StatePublished - Mar 4 2017
Externally publishedYes

Bibliographical note

Funding Information:
G. McGrew was supported by NSF Grant EMSW21-MCTP 0636528. J. Davis was supported by NSF Grant EMSW21-MCTP 0636528. D. Steele was supported by NSF Grant EMSW21-MCTP 0636528. K. Marsten was supported by NSF Grant EMSW21-MCTP 0636528.

Publisher Copyright:
© 2016 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

  • Boolean
  • concatenation
  • derivative
  • functions
  • Nonlinearity

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