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

15 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

Bibliographical note

Funding Information:
Acknowledgments The first and third named authors were supported by Priority Research Centers Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2009-0093827). The first named author was also supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MEST) (No. 2011-0010328) and the second named author was also supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MEST) (No. 2011-0015684). The authors would like to thank the anonymous referees for their helpful comments for the clarity of this paper. The authors also would like to thank Hyun Jin Kim for providing us with Table 2.

Keywords

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

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