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Computes the autocorrelation of a sequence S,
where S must have universe GF(2).
The autocorrelation is defined to be
C(t) = ∑i=1L ( - 1) S[i] + S[i + t]
where L is the length of the sequence, and the values
of S[i + t] wrap around to the beginning of the sequence
when i + t > L.
It is well known that the LFSR's with maximal periods have nice
autocorrelation properties. This is illustrated below.
> C<D> := PrimitivePolynomial (GF(2), 5);
> C;
D^5 + D^2 + 1
> s := [GF(2)|1,1,1,1,1];
> t := LFSRSequence(C, s, 31);
> t;
[ 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0,
1, 1, 0, 0, 0 ]
> AutoCorrelation (t, 2);
-1
Computes the crosscorrelation of two binary sequences S1 and S2,
where S1 and S2 must each have universe GF(2), and they must have
the same length L.
The crosscorrelation is defined to be:
C(t) = ∑i=1L ( - 1) S1[i] + S2[i + t]
and the values of S2[i + t] wrap around to the beginning of the sequence
when i + t > L.
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