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- W4379116777 abstract "Binary <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>m</i> -sequences are those with the largest period <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</i> = 2 <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><i>m</i></sup> –1 among the binary sequences produced by linear shift registers with length <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>m</i> . They have a wide range of applications in communication since they have several desirable pseudorandom properties, such as balance, uniform pattern distribution, and ideal (classical) autocorrelation. In 1967, Mandelbaum introduced a 2-adic version of classical autocorrelation of binary sequences, called arithmetic autocorrelation, in his research on arithmetic codes. Later, Goresky and Klapper generalized this notion to the nonbinary case and got several properties of arithmetic autocorrelation related to linear shift registers with carry. Recently, Z. Chen et al. showed an upper bound on the arithmetic autocorrelation of binary <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>m</i> -sequences and raised a conjecture on the absolute value distribution of the arithmetic autocorrelation of binary <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>m</i> -sequences. In this paper, we present a general formula for computing arithmetic autocorrelation, from which we completely determine the arithmetic autocorrelation distribution of arbitrary binary <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>m</i> -sequences. In particular, the conjecture raised by Z. Chen et al. is verified." @default.
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- W4379116777 date "2023-09-01" @default.
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- W4379116777 title "Arithmetic Autocorrelation Distribution of Binary <i> <b>m</b> </i>-Sequences" @default.
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- W4379116777 doi "https://doi.org/10.1109/tit.2023.3282229" @default.
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