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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
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.
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
KEYWORD
nonn,hard,nice,more
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 April 24 22:17 EDT 2024. Contains 371964 sequences. (Running on oeis4.)