A053168 Hamming weights (or nonlinearity) of degree 4 rotation-symmetric functions.

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

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

Table of n, a(n) for n=4..13.

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

Cf. A051253.

Sequence in context: A255464 A325998 A322216 * A141388 A255473 A255295

Adjacent sequences: A053165 A053166 A053167 * A053169 A053170 A053171

Keyword

hard,more,nonn

Author

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

Status

approved