0,1

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

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.]

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.]

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).]

B. Preneel, Analysis and design of cryptographic hash functions, Ph. D. thesis, Katholieke Universiteit Leuven, Belgium, 1993. [Confirms a(3).]

O. S. Rothaus, On "bent" functions, J. Combinat. Theory, 20A (1976), 300-305.

Philippe Langevin, Classification of Boolean Quartics Forms in Eight Variables

Meng Qing-shu, Yang Zhang and Cui Jing-song, A novel algorithm enumerating bent functions, (2004). [Also confirms a(3).]

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.

See A099090 for a normalized version.

Sequence in context: A076985 A120802 A120838 this_sequence A132573 A061591 A103085

Adjacent sequences: A004488 A004489 A004490 this_sequence A004492 A004493 A004494

nonn,hard,nice

N. J. A. Sloane (njas(AT)research.att.com), Sep 23 2008, based on emails from Philippe Langevin, Gregor Leander and Pante Stanica.

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