A207676 Nonlinearities of 3-variable Boolean functions ordered lexicographically.

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

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: A026606 A372469 A265918 * A161175 A356515 A095955

Adjacent sequences: A207673 A207674 A207675 * A207677 A207678 A207679

Keyword

nonn,fini,full

Author

Erdener Uyan, Feb 19 2012

Status

approved