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Upper and Lower Bounds on Maximum Nonlinearity of n-input m-output Boolean Function

Authors
  • Wadayama, Tadashi1
  • Hada, Toru2
  • Wakasugi, Koichiro2
  • Kasahara, Masao2
  • 1 Okayama Prefectural University, Faculty of Computer Science and System Engineering, 111, Kuboki, Soja, Okayama, 719-1197, Japan , Okayama
  • 2 Kyoto Institute of Technology, Matugasaki, Kyoto, 606-8585, Japan , Kyoto
Type
Published Article
Journal
Designs, Codes and Cryptography
Publisher
Kluwer Academic Publishers
Publication Date
May 01, 2001
Volume
23
Issue
1
Pages
23–34
Identifiers
DOI: 10.1023/A:1011207501748
Source
Springer Nature
Keywords
License
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Abstract

The paper presents lower and upper bounds on the maximumnonlinearity for an n-input m-output Booleanfunction. We show a systematic construction method for a highlynonlinear Boolean function based on binary linear codes whichcontain the first order Reed-Muller code as a subcode. We alsopresent a method to prove the nonexistence of some nonlinearBoolean functions by using nonexistence results on binary linearcodes. Such construction and nonexistence results can be regardedas lower and upper bounds on the maximum nonlinearity. For somen and m, these bounds are tighter than theconventional bounds. The techniques employed here indicate astrong connection between binary linear codes and nonlinear n-input m-output Boolean functions.

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