Arithmetic Crosscorrelation of Pseudorandom Binary Sequences of Coprime Periods

Chen, Zhixiong; Niu, Zhihua; Winterhof, Arne

doi:10.1109/tit.2022.3184176

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2024

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“…[13,14]. Chen, Niu and Winterhof (partially with other coauthors) considered the arithmetic auto-correlation of binary m-sequences [15] and the arithmetic cross-correlation of binary sequences with coprime periods [16].…”

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confidence: 99%

Arithmetic correlation of binary half‐ℓ‐sequences

Chen

Edemskiy

Niu

et al. 2022

IET Information Security

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The arithmetic correlations of two binary half‐ℓ‐sequences with connection integer pr, which is an odd prime power, are investigated. Possible values (of the arithmetic correlation) are calculated. In particular, if p ≡ 1 (mod 8), the authors prove that they are zero for non‐trivial shifts, that is, the half‐ℓ‐sequences have ideal arithmetic correlations. If p ≡ −1 (mod 8), an upper bound, which is of order of magnitude pr−1/2 ln p, is derived by using earlier results on the imbalance of half‐ℓ‐sequences with connection integer p studied by Gu and Klapper and later improved by Wang and Tan.

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