STATISTICAL PROPERTIES OF THE ARITHMETIC CORRELATION OF SEQUENCES
Mark Goresky, Andrew Klapper · International Journal of Foundations of Computer Science · 2011
In this paper we study arithmetic correlations of sequences. Arithmetic correlations are the with-carry analogs of classical correlations. We analyze the arithmetic autocorrelations of non-binary ℓ-sequences, showing that they are nearly optimal. We analyze the expected auto- and cross-correlations of sequences with fixed shift, averaged over all sequences with a fixed period. We analyze the expected autocorrelations of a fixed sequence, averaged over all shifts.