Some Results on the Arithmetic Correlation of Sequences - Sequences and Their Applications-SETA 2008 - page 80

6 Conclusions

We have analyzed the autocorrelations of -sequences and the expected arith-
metic auto- and cross-correlations for fixed shift, and we have characterized
arithmetic shift and add sequences. In all these cases the answers are similar to
the answers in the classical (no carry) case.
Two problems are left open here. First, we have not computed the arithmetic
cross-correlations of non-binary sequences. In the binary case, this is one instance
where the answer in the arithmetic realm is radically different from the answer
in the classical realm.
Second, we have not computed the second moment and variance of the arith-
metic autocorrelation. This appears to be a much harder problem than comput-
ing the expected arithmetic auto- and cross-correlations or the second moment
of the arithmetic cross-correlation.

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