2022/11/30 by Jing, Xiaoyan, Zhang, Aixian, Feng, Keqin
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2211.16766
Binary m-sequences are ones with the largest period n=2m-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 \cite9Mand introduces a 2-adic version of classical autocorrelation of binary sequences, called arithmetic autocorrelation. Later, Goresky and Klapper \cite3G1,4G2,5G3,6G4 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. \cite1C1 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.