

A207676


Nonlinearities of 3variable 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
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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 3variables.
Also the list of first 2^2^3 terms of rth order nonlinearity values of Boolean functions of (r+2)variables in lexicographic order of their truth tables.


LINKS



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


KEYWORD

nonn,fini,full


AUTHOR



STATUS

approved



