Search: id:A004491
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%I A004491
%S A004491 2,8,896,5425430528,99270589265934370305785861242880
%N A004491 Number of bent functions of 2n variables.
%C A004491 The old entry with this sequence number was a duplicate of A004483.
%D A004491 Berlekamp, Elwyn R. and Welch, Lloyd R., 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.]
%D A004491 J. F. Dillon, Elementary Hadamard Difference Sets, Ph. D. Thesis, Univ. 
               Maryland, 1974.
%D A004491 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 A004491 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 A004491 Maiorana, James A., A classification of the cosets of the Reed-Muller 
               code R(1,6), Math. Comp. 57 (1991), no. 195, 403-414. [Gives a(3).]
%D A004491 B. Preneel, Analysis and design of cryptographic hash functions, Ph. 
               D. thesis, Katholieke Universiteit Leuven, Belgium, 1993. [Confirms 
               a(3).]
%D A004491 O. S. Rothaus, On "bent" functions, J. Combinat. Theory, 20A (1976), 
               300-305.
%H A004491 Philippe Langevin, <a href="http://langevin.univ-tln.fr/project/quartics/
               ">Classification of Boolean Quartics Forms in Eight Variables</a>
%H A004491 Meng Qing-shu, Yang Zhang and Cui Jing-song, <a href="http://eprint.iacr.org/
               2004/274.pdf">A novel algorithm enumerating bent functions</a>, (2004). 
               [Also confirms a(3).]
%H A004491 N. J. A. Sloane and R. J. Dick, <a href="http://www.research.att.com/
               ~njas/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 A004491 See A099090 for a normalized version.
%Y A004491 Sequence in context: A076985 A120802 A120838 this_sequence A132573 A061591 
               A103085
%Y A004491 Adjacent sequences: A004488 A004489 A004490 this_sequence A004492 A004493 
               A004494
%K A004491 nonn,hard,nice
%O A004491 0,1
%A A004491 N. J. A. Sloane (njas(AT)research.att.com), Sep 23 2008, based on emails 
               from Philippe Langevin, Gregor Leander and Pante Stanica.
%E A004491 a(4) found in 2008 by Philippe Langevin and Gregor Leander.

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