

A004491


Number of bent functions of 2n variables.


1




OFFSET

0,1


COMMENTS

The old entry with this sequence number was a duplicate of A004483.


REFERENCES

J. F. Dillon, Elementary Hadamard Difference Sets, Ph. D. Thesis, Univ. Maryland, 1974.
J. F. Dillon, Elementary Hadamard Difference Sets, in Proc. 6th SouthEastern Conf. Combin. Graph Theory Computing (Utilitas Math., Winnipeg, 1975), pp. 237249.
F. J. MacWilliams and N. J. A. Sloane, The Theory of ErrorCorrecting 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

Table of n, a(n) for n=0..4.
Elwyn R. Berlekamp and Lloyd R.Welch, Weight distributions of the cosets of the (32,6) ReedMuller code, IEEE Trans. Information Theory IT18 (1972), 203207. [Not strictly relevant because it deals with the case of five variables. Included for completeness.]
Philippe Langevin, Classification of Boolean Quartics Forms in Eight Variables
James A. Maiorana, A classification of the cosets of the ReedMuller code R(1,6), Math. Comp. 57 (1991), no. 195, 403414. [Gives a(3).]
Meng Qingshu, Yang Zhang and Cui Jingsong, 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), 300305.
N. J. A. Sloane and R. J. Dick, On the Enumeration of Cosets of FirstOrder ReedMuller Codes, Proc. IEEE International Conf. Commun., Montreal 1971, IEEE Press, NY, 7 (1971), pp. 362 to 366.


CROSSREFS

See A099090 for a normalized version.
Sequence in context: A120802 A120838 A282890 * A132573 A322142 A061591
Adjacent sequences: A004488 A004489 A004490 * A004492 A004493 A004494


KEYWORD

nonn,hard,nice


AUTHOR

N. J. A. Sloane, Sep 23 2008, based on emails from Philippe Langevin, Gregor Leander and Pante Stanica.


EXTENSIONS

a(4) found in 2008 by Philippe Langevin and Gregor Leander.


STATUS

approved



