A001289 Number of equivalence classes of Boolean functions modulo linear functions.

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

Offset

1,2

Comments

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.

References

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.

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

Links

Table of n, a(n) for n=1..7.

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.

An Braeken, Yuri Borissov, Svetla Nikova and Bart Preneel, Classification of Boolean Functions of 6 Variables or Less with Respect to Cryptographic Properties, IACR, Report 2004/248, 2004-2005.

L. E. Danielsen, Database of Boolean functions

Xiang-Dong Hou, AGL(m,2) acting on R(r,m)/R(s,m), J. Algebra, 171 (1995), 921-938.

I. Strazdins, Universal affine classification of Boolean functions, Acta Applic. Math. 46 (1997), 147-167.

Index entries for sequences related to Boolean functions

Crossrefs

Cf. A109003.

Sequence in context: A066084 A141319 A369602 * A103045 A126464 A041979

Adjacent sequences: A001286 A001287 A001288 * A001290 A001291 A001292

Keyword

nonn,hard,more,nice

Author

N. J. A. Sloane.

Extensions

a(7) from Hou (1995)

Status

approved