Boolean functions with MacWilliams duality

Jong Yoon Hyun, Heisook Lee, Yoonjin Lee

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We introduce a new class of Boolean functions for which the MacWilliams duality holds, called MacWilliams-dual functions, by considering a dual notion on Boolean functions. By using the MacWilliams duality, we prove the Gleason-type theorem on MacWilliams-dual functions. We show that a collection of MacWilliams-dual functions contains all the bent functions and all formally self-dual functions. We also obtain the Pless power moments for MacWilliams-dual functions. Furthermore, as an application, we prove the nonexistence of bent functions in 2n variables with minimum degree n-k for any nonnegative integer k and n ≥ N with some positive integer N under a certain condition.

Original languageEnglish
Pages (from-to)273-287
Number of pages15
JournalDesigns, Codes, and Cryptography
Issue number2
StatePublished - Aug 2014


  • Bent function
  • Formally self-dual function
  • Formally self-dual pair
  • MacWilliams duality
  • MacWilliams-dual function
  • Self-dual bent function


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