Constant amplitude zero auto-correlation (CAZAC) sequences are widely applied in waveforms for radar and communication systems. Motivated by a recent work [Berggren and Popović, IEEE Trans. Inf. Theory 70(8), 6068-6075 (2024)], this paper further investigates the approach to generating CAZAC sequences by interleaving Zadoff-Chu (ZC) sequences with permutation polynomials (PPs). We propose one class of high-degree PPs over the integer ring Z N , and utilize them and their inverses to interleave ZC sequences for constructing CAZAC sequences. It is known that a CAZAC sequence can be extended to an equivalence class by five basic opertations. We further show that the obtained CAZAC sequences are not covered by the equivalence classes of ZC sequences and interleaved ZC sequences by quadratic PPs and their inverses, and prove the sufficiency of the conjecture by Berggren and Popović in the aforementioned work. In addition, we also evaluate the aperiodic auto-correlation of certain ZC sequences from quadratic PPs.

翻译：恒包络零自相关（CAZAC）序列在雷达与通信系统的波形设计中具有广泛应用。受近期研究[Berggren and Popović, IEEE Trans. Inf. Theory 70(8), 6068-6075 (2024)]的启发，本文进一步探讨了通过置换多项式（PPs）交织Zadoff-Chu（ZC）序列来生成CAZAC序列的方法。我们提出了一类定义在整数环Z_N上的高次置换多项式，并利用这些多项式及其逆多项式对ZC序列进行交织以构造CAZAC序列。已知CAZ序列可通过五种基本操作扩展为等价类。我们进一步证明：所获得的CAZAC序列未被ZC序列的等价类、以及由二次置换多项式及其逆多项式构造的交织ZC序列的等价类所覆盖，从而证明了Berggren与Popović在上述工作中所提出猜想的充分性。此外，我们还评估了由二次置换多项式生成的特定ZC序列的非周期自相关特性。