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 language | English |
|---|---|
| Pages (from-to) | 295-304 |
| Number of pages | 10 |
| Journal | Designs, Codes, and Cryptography |
| Volume | 63 |
| Issue number | 3 |
| DOIs | |
| State | Published - 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