Arithmetic autocorrelation and pattern distribution of binary sequences

Abstract

We clarify a relation between the arithmetic autocorrelation and pattern distribution of binary sequences, then we apply the relation to study the upper bound of arithmetic autocorrelation for two binary sequences constructed by Fermat quotient and the generalized cyclotomic class of order $ 2 $, respectively. Our results indicate that the sequences with large 'long term' correlations may have small 'short term' pattern distribution; and thus have rather small arithmetic autocorrelations.

Keywords

• arithmetic autocorrelation
• fermat quotient
• generalized cyclotomic
• binary sequence
• character sum