A004491 Number of bent functions of 2n variables.
2, 8, 896, 5425430528, 99270589265934370305785861242880
Offset: 0
References
- Carlet, C. & Mesnager, S., Four decades of research on bent functions, Designs, Codes and Cryptography, January 2016, Volume 78, Issue 1, pp. 5-50.
- J. F. Dillon, Elementary Hadamard Difference Sets, Ph. D. Thesis, Univ. Maryland, 1974.
- J. F. Dillon, Elementary Hadamard Difference Sets, in Proc. 6th South-Eastern Conf. Combin. Graph Theory Computing (Utilitas Math., Winnipeg, 1975), pp. 237-249.
- F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1977. [Section 5 of Chap. 14 deals with bent functions. For a(2) see page 418.]
- B. Preneel, Analysis and design of cryptographic hash functions, Ph. D. thesis, Katholieke Universiteit Leuven, Belgium, 1993. [Confirms a(3).]
Links
- Elwyn R. Berlekamp and Lloyd R.Welch, Weight distributions of the cosets of the (32,6) Reed-Muller code, IEEE Trans. Information Theory IT-18 (1972), 203-207. [Not strictly relevant because it deals with the case of five variables. Included for completeness.]
- L. Budaghyan and P. Stanica, What is a cryptographic Boolean function?, Notices Amer. Math. Soc., 66 (Jan 2019), 60-63.
- Philippe Langevin, Classification of Boolean Quartics Forms in Eight Variables [Broken link]
- James A. Maiorana, A classification of the cosets of the Reed-Muller code R(1,6), Math. Comp. 57 (1991), no. 195, 403-414. [Gives a(3).]
- Meng Qing-shu, Yang Zhang and Cui Jing-song, A novel algorithm enumerating bent functions, IACR, Report 2004/274, 2004. [Also confirms a(3).]
- O. S. Rothaus, On "bent" functions, J. Combinat. Theory, 20A (1976), 300-305.
- N. J. A. Sloane and R. J. Dick, On the Enumeration of Cosets of First-Order Reed-Muller Codes, Proc. IEEE International Conf. Commun., Montreal 1971, IEEE Press, NY, 7 (1971), pp. 36-2 to 36-6.
Crossrefs
See A099090 for a normalized version.
Extensions
a(4) found in 2008 by Philippe Langevin and Gregor Leander.
Comments