%I #16 Feb 11 2018 03:06:17

%S 1,2,3,8,48,150357,63379147320777408548

%N Number of equivalence classes of Boolean functions modulo linear functions.

%C Number of equivalence classes of all 2^(2^n) maps from GF(2)^n to GF(2), where maps f and g are equivalent iff there exists an invertible n X n binary matrix M, two n-dimensional binary vectors a and b and a binary scalar c such that g(x) = f(Mx+a) + b.x + c.

%D R. J. Lechner, Harmonic Analysis of Switching Functions, in A. Mukhopadhyay, ed., Recent Developments in Switching Theory, Acad. Press, 1971, pp. 121-254, esp. p. 186.

%D F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1977, p. 431.

%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.

%H An Braeken, Yuri Borissov, Svetla Nikova and Bart Preneel, <a href="https://ia.cr/2004/248">Classification of Boolean Functions of 6 Variables or Less with Respect to Cryptographic Properties</a>, IACR, Report 2004/248, 2004-2005.

%H L. E. Danielsen, <a href="http://www.ii.uib.no/~larsed/boolean/">Database of Boolean functions</a>

%H Xiang-Dong Hou, <a href="https://doi.org/10.1006/jabr.1995.1043">AGL(m,2) acting on R(r,m)/R(s,m)</a>, J. Algebra, 171 (1995), 921-938.

%H I. Strazdins, <a href="http://dx.doi.org/10.1023/A:1005769927571">Universal affine classification of Boolean functions</a>, Acta Applic. Math. 46 (1997), 147-167.

%H <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>

%Y Cf. A109003.

%K nonn,hard,more,nice

%O 1,2

%A _N. J. A. Sloane_.

%E a(7) from Hou (1995)