A000614 Number of complemented types of Boolean functions of n variables under action of AG(n,2).

2, 3, 6, 18, 206, 7888299, 8112499583888855378066, 42287533217833953489054778023401252726576585396037133766

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Comments

From Philippe Langevin's article: Let m be a positive integer. The space of Boolean functions from GF(2)^m into GF(2) is denoted by RM(k,m). This notation comes from coding theory, where it is the Reed-Muller code of order k in m variables. The affine group AG(2, m) acts on the spaces RM(k,m), and thus on RM(k,m)/RM(s,m) when s <= k. - Jonathan Vos Post, Feb 08 2011

References

• R. J. Lechner, Harmonic Analysis of Switching Functions, in A. Mukhopadhyay, ed., Recent Developments in Switching Theory, Ac. Press, 1971, pp. 121-254, esp. p. 186.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• M. A. Harrison, The number of equivalence classes of Boolean functions under groups containing negation, IEEE Trans. Electron. Comput. 12 (1963), 559-561.
• M. A. Harrison, The number of equivalence classes of Boolean functions under groups containing negation, IEEE Trans. Electron. Comput. 12 (1963), 559-561. [Annotated scanned copy]
• M. A. Harrison, On the classification of Boolean functions by the general linear and affine groups, J. Soc. Indust. Appl. Math. 12 (1964) 285-299.
• Philippe Langevin, Classification of Boolean functions under the affine group, Oct 31, 2009.
• Index entries for sequences related to Boolean functions

Crossrefs

Cf. A000214.

Extensions

More terms and better description from Vladeta Jovovic, Feb 24 2000