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A004491 Number of bent functions of 2n variables. 1
2, 8, 896, 5425430528, 99270589265934370305785861242880 (list; graph; refs; listen; history; text; internal format)
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 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

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) 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.]

Philippe Langevin, Classification of Boolean Quartics Forms in Eight Variables

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.

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

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Last modified June 25 10:10 EDT 2019. Contains 324351 sequences. (Running on oeis4.)