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A207328 Nonlinearities of 4-variable boolean functions ordered lexicographically. 1
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, 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, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 3, 2, 3, 3, 4, 3, 4, 4 (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 a boolean function.

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

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.

LINKS

Erdener Uyan, Table of n, a(n) for n = 0..65535 (complete sequence)

EXAMPLE

n in GF(2^4)

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

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

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

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

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,

1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,3,2,3,3,4,3,4,4,3,3,4,4,3,4,3,3,2...

PROG

(R w/ boolfun package)

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

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

a[n]<-nl(f)

}

CROSSREFS

Cf. A207676 (that of 3-variable boolean functions).

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: A105111 A105112 A105113 * A105056 A105061 A105164

Adjacent sequences:  A207325 A207326 A207327 * A207329 A207330 A207331

KEYWORD

nonn

AUTHOR

Erdener Uyan, Feb 28 2012

STATUS

approved

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Last modified January 17 23:37 EST 2020. Contains 330995 sequences. (Running on oeis4.)