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A207676 Nonlinearities of 3-variable boolean functions ordered lexicographically. 2
0, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 0, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 0, 1, 2, 2, 1, 1, 2, 2, 1, 0, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 0, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Nonlinearity of a boolean function is its minimum Hamming distance to the elements of the set of affine boolean functions.

In this sequence, n represents the truth table of Boolean functions.

There are 2^2^3 = 256 terms in this list, i.e. the number of boolean functions of 3-variables.

Also the list of first 2^2^3 terms of r-th order nonlinearity values of boolean functions of (r+2)-variables in lexicographic order of their truth tables.

LINKS

Erdener Uyan, Table of n, a(n) for n = 0..255 (complete sequence)

EXAMPLE

n in GF(2^3) a(1)=a((00000001)_2)=1;a(5)=a((00000101)_2)=2;a(15)=a((00001111)_2)=0;

This can be written as a triangle, though having few outliers:

0,

1,

1,2,

1,2,2,1,

1,2,2,1,2,1,1,0,

1,2,2,1,2,1,1,2,2,1,1,2,1,2,2,1,

1,2,2,1,2,1,1,2,2,1,1,2,1,2,2,1,2,1,1,0,1,2,2,1,1,2,2,1,0,1,1,2,...

PROG

(R w/ boolfun package)

for(n in 0:2^(2^3)-1){

f<- BooleanFunction(toBin(n, 2^3))

a[n]<-nl(f)

}

CROSSREFS

Cf. A000120, A000069, A001969, A007088 (sequences dealing with binary expansion of n).

Cf. A051253, A053168, A053189 (sequences that relate nonlinearity with Hamming weight for a special class of boolean functions).

Sequence in context: A054350 A026606 A265918 * A161175 A095955 A272772

Adjacent sequences:  A207673 A207674 A207675 * A207677 A207678 A207679

KEYWORD

nonn,fini,full

AUTHOR

Erdener Uyan, Feb 19 2012

STATUS

approved

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Last modified February 28 01:30 EST 2020. Contains 332319 sequences. (Running on oeis4.)