Arithmetic correlation of binary half‐ ℓ ‐sequences
Zhixiong Chen, Vladimir Edemskiy, Zhihua Niu, Yuqi Sang · IET Information Security · 2022
Abstract The arithmetic correlations of two binary half‐ ℓ ‐sequences with connection integer p r , 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 p r −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.