This paper presents a direct construction of an optimal symmetrical Z-complementary code set (SZCCS) of prime power lengths using a multi-variable function (MVF). SZCCS is a natural extension of the Z-complementary code set (ZCCS), which has only front-end zero correlation zone (ZCZ) width. SZCCS has both front-end and tail-end ZCZ width. SZCCSs are used in developing optimal training sequences for broadband generalized spatial modulation systems over frequency-selective channels because they have ZCZ width on both the front and tail ends. The construction of optimal SZCCS with large set sizes and prime power lengths is presented for the first time in this paper. Furthermore, it is worth noting that several existing works on ZCCS and SZCCS can be viewed as special cases of the proposed construction.

翻译：本文提出了一种利用多变量函数直接构造素数幂长度最优对称Z互补码集的方法。对称Z互补码集是Z互补码集的自然扩展，后者仅具有前端零相关区宽度，而前者同时具备前端和尾端零相关区宽度。由于在频率选择性信道上的宽带广义空间调制系统中，对称Z互补码集的前端和尾端均具有零相关区宽度，因此被用于开发最优训练序列。本文首次提出了具有大集合规模和素数幂长度的最优对称Z互补码集的构造方法。值得注意的是，现有若干关于Z互补码集和对称Z互补码集的研究工作可视为本文所提构造的特例。