# Arithmetic autocorrelation distribution of binary m-sequences

Binary m-sequences are ones with the largest period n=2^m-1 among the binary sequences produced by linear shift registers with length m. They have a wide range of applications in communication since they have several desirable pseudorandomness such as balance, uniform pattern distribution and ideal (classical) autocorrelation. In his reseach on arithmetic codes, Mandelbaum <cit.> introduces a 2-adic version of classical autocorrelation of binary sequences, called arithmetic autocorrelation. Later, Goresky and Klapper <cit.> generalize this notion to nonbinary case and develop several properties of arithmetic autocorrelation related to linear shift registers with carry. Recently, Z. Chen et al. <cit.> show an upper bound on arithmetic autocorrelation of binary m-sequences and raise a conjecture on absolute value distribution on arithmetic autocorrelation of binary m-sequences.

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