A new set of polyphase sequences with low correlation and low ambiguity function

Sequences with low correlation and low ambiguity function magnitude play a pivotal role in both wireless communication and radar systems. In this paper, we propose a new set of polyphase sequences over Galois rings. Precisely derive the size of the sequence set, its correlation, and the ambiguity function magnitude. The proposed generalized sequences have period $ N = p^n-1 $, family size $ M\geq\frac{p^{nm}(p^{ne}-1)}{p^n-1} $, the maximum correlation magnitude $ \theta_{\text{max}} \leq \max\left\{p^{e-1}-1, p^{j-1}(1+p^m)-1\right\}\sqrt{p^n}+1 $, and the maximum ambiguity magnitude $ \widehat{\theta}_{\text{max}} \leq \max\left\{p^{e-1}, p^{j-1}(1+p^m)\right\}\sqrt{p^n} $, where $ p $ is any prime, $ n $ and $ e $ are positive integers, $ e<\frac{n+2}{2} $, $ 1\leq j \leq e-1 $ and $ 0\leq m <\frac{n+2}{2}-j $.