MacWilliams duality and a Gleason-type theorem on self-dual bent functions

Jong Yoon Hyun, Heisook Lee, Yoonjin Lee

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

We prove that the MacWilliams duality holds for bent functions. It enables us to derive the concept of formally self-dual Boolean functions with respect to their near weight enumerators. By using this concept, we prove the Gleason-type theorem on self-dual bent functions. As an application, we provide the total number of (self-dual) bent functions in two and four variables obtaining from formally self-dual Boolean functions.

Original languageEnglish
Pages (from-to)295-304
Number of pages10
JournalDesigns, Codes, and Cryptography
Volume63
Issue number3
DOIs
StatePublished - Jun 2012

Keywords

  • Formally self-dual boolean function
  • Gleason theorem
  • MacWilliams duality
  • Self-dual bent function

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