OFFSET
4,2
COMMENTS
T. W. Cusick and P. Stanica conjectured that the Hamming weight and the nonlinearity are the same for rotation-symmetric functions of degree 3. We conjecture that the same is true for rotation-symmetric functions of any degree.
The conjecture is true for all such functions of degree >= 3 and at most 13 variables. - Charlie Neder, Feb 05 2019
LINKS
T. W. Cusick and P. Stanica, Fast Evaluation, Weights and Nonlinearity of Rotation-Symmetric Functions, Discr. Math. 258 (2002), 289-301.
EXAMPLE
a(4)=1, since the weight (or nonlinearity) of x1*x2*x3*x4 is 1.
a(5)=6, since the weight (or nonlinearity) of x1*x2*x3*x4+x2*x3*x4*x5+x3*x4*x5*x1+x4*x5*x1*x2+x5*x1*x2*x3 is 6.
CROSSREFS
KEYWORD
hard,more,nonn
AUTHOR
Pantelimon Stanica (pstanica(AT)mail.aum.edu), Feb 29 2000
STATUS
approved