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Hamming weights (or nonlinearity) of degree 4 rotation-symmetric functions.
3

%I #14 Feb 05 2019 01:42:24

%S 1,6,6,22,40,100,200,452,936,2016

%N Hamming weights (or nonlinearity) of degree 4 rotation-symmetric functions.

%C 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.

%C The conjecture is true for all such functions of degree >= 3 and at most 13 variables. - _Charlie Neder_, Feb 05 2019

%H T. W. Cusick and P. Stanica, <a href="http://dx.doi.org/10.1016/S0012-365X(02)00354-0">Fast Evaluation, Weights and Nonlinearity of Rotation-Symmetric Functions</a>, Discr. Math. 258 (2002), 289-301.

%e a(4)=1, since the weight (or nonlinearity) of x1*x2*x3*x4 is 1.

%e 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.

%Y Cf. A051253.

%K hard,more,nonn

%O 4,2

%A Pantelimon Stanica (pstanica(AT)mail.aum.edu), Feb 29 2000