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A053168 Hamming weights (or nonlinearity) of degree 4 rotation-symmetric functions. 3
1, 6, 6, 22, 40, 100, 200, 452, 936, 2016 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 18 09:15 EST 2020. Contains 332011 sequences. (Running on oeis4.)