A207328 - OEIS

%I #25 Jan 04 2021 19:53:05

%S 0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,3,1,2,

%T 2,3,2,3,3,4,2,3,3,4,3,4,4,3,2,3,3,4,3,4,4,3,3,4,4,3,4,3,3,2,1,2,2,3,

%U 2,3,3,4,2,3,3,4,3,4,4,3,2,3,3,4,3,4,4

%N Nonlinearities of 4-variable Boolean functions ordered lexicographically.

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

%C In this sequence, n represents the truth table of a Boolean function.

%C There are 2^2^4 = 65536 terms in this list, i.e. the number of 4-variable Boolean functions.

%C This is also the list of first 2^2^4 terms of r-th order nonlinearity values of (r+3)-variables Boolean functions ordered lexicographically.

%H Erdener Uyan, <a href="/A207328/b207328.txt">Table of n, a(n) for n = 0..65535</a> (complete sequence)

%e n in GF(2^4)

%e a(1)=a((0000000000000001)_2)=1;

%e a(5)=a((0000000000000101)_2)=2;

%e a(15)=a((0000000000001111)_2)=0;

%e This can also be written as a triangle, though contains outliers in later iterations:

%e 0,

%e 1,

%e 1,2,

%e 1,2,2,3,

%e 1,2,2,3,2,3,3,4,

%e 1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,3,

%e 1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,3,2,3,3,4,3,4,4,3,3,4,4,3,4,3,3,2...

%o (R w/ boolfun package)

%o for(n in 0:2^(2^4)-1){

%o f<- BooleanFunction(toBin(n,2^4))

%o a[n]<-nl(f)

%o }

%Y Cf. A207676 (that of 3-variable Boolean functions).

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

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

%K nonn

%O 0,4

%A _Erdener Uyan_, Feb 28 2012