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A053168
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Hamming weights (or nonlinearity) of degree 4 rotation-symmetric functions.
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3
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OFFSET
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4,2
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COMMENTS
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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
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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hard,more,nonn
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AUTHOR
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Pantelimon Stanica (pstanica(AT)mail.aum.edu), Feb 29 2000
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STATUS
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approved
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