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%I #27 May 13 2021 14:23:05
%S 2,8,896,5425430528,99270589265934370305785861242880
%N Number of bent functions of 2n variables.
%C The old entry with this sequence number was a duplicate of A004483.
%D Carlet, C. & Mesnager, S., Four decades of research on bent functions, Designs, Codes and Cryptography, January 2016, Volume 78, Issue 1, pp. 5-50.
%D J. F. Dillon, Elementary Hadamard Difference Sets, Ph. D. Thesis, Univ. Maryland, 1974.
%D J. F. Dillon, Elementary Hadamard Difference Sets, in Proc. 6th South-Eastern Conf. Combin. Graph Theory Computing (Utilitas Math., Winnipeg, 1975), pp. 237-249.
%D 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.]
%D B. Preneel, Analysis and design of cryptographic hash functions, Ph. D. thesis, Katholieke Universiteit Leuven, Belgium, 1993. [Confirms a(3).]
%H Elwyn R. Berlekamp and Lloyd R.Welch, <a href="https://doi.org/10.1109/TIT.1972.1054732">Weight distributions of the cosets of the (32,6) Reed-Muller code</a>, IEEE Trans. Information Theory IT-18 (1972), 203-207. [Not strictly relevant because it deals with the case of five variables. Included for completeness.]
%H L. Budaghyan and P. Stanica, <a href="https://www.ams.org/journals/notices/201901/201901FullIssue.pdf">What is a cryptographic Boolean function?</a>, Notices Amer. Math. Soc., 66 (Jan 2019), 60-63.
%H Philippe Langevin, <a href="http://langevin.univ-tln.fr/project/quartics/">Classification of Boolean Quartics Forms in Eight Variables</a> [Broken link]
%H James A. Maiorana, <a href="https://doi.org/10.1090/S0025-5718-1991-1079027-8">A classification of the cosets of the Reed-Muller code R(1,6)</a>, Math. Comp. 57 (1991), no. 195, 403-414. [Gives a(3).]
%H Meng Qing-shu, Yang Zhang and Cui Jing-song, <a href="https://ia.cr/2004/274">A novel algorithm enumerating bent functions</a>, IACR, Report 2004/274, 2004. [Also confirms a(3).]
%H O. S. Rothaus, <a href="https://doi.org/10.1016/0097-3165(76)90024-8">On "bent" functions</a>, J. Combinat. Theory, 20A (1976), 300-305.
%H N. J. A. Sloane and R. J. Dick, <a href="http://neilsloane.com/doc/dick.html">On the Enumeration of Cosets of First-Order Reed-Muller Codes</a>, Proc. IEEE International Conf. Commun., Montreal 1971, IEEE Press, NY, 7 (1971), pp. 36-2 to 36-6.
%Y See A099090 for a normalized version.
%K nonn,hard,nice,more
%O 0,1
%A _N. J. A. Sloane_, Sep 23 2008, based on emails from Philippe Langevin, Gregor Leander and Pante Stanica.
%E a(4) found in 2008 by Philippe Langevin and Gregor Leander.
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