The rapid progression in wireless communication technologies, especially in multicarrier code-division multiple access (MC-CDMA), there is a need of advanced code construction methods. Traditional approaches, mainly based on generalized Boolean functions, have limitations in code length versatility. This paper introduces a novel approach to constructing complete complementary codes (CCC) and Z-complementary code sets (ZCCS), for reducing interference in MC-CDMA systems. The proposed construction, distinct from Boolean function-based approaches, employs additive characters over Galois fields GF($p^{r}$), where $p$ is prime and $r$ is a positive integer. First, we develop CCCs with lengths of $p^{r}$, which are then extended to construct ZCCS with both unreported lengths and sizes of $np^{r}$, where $n$ are arbitrary positive integers. The versatility of this method is further highlighted as it includes the lengths of ZCCS reported in prior studies as special cases, underscoring the method's comprehensive nature and superiority.

翻译：无线通信技术的快速发展，特别是多载波码分多址（MC-CDMA）中，亟需先进的码构造方法。传统方法主要基于广义布尔函数，在码长多样性方面存在局限性。本文提出一种新颖的完全互补码（CCC）和Z互补码集（ZCCS）构造方法，用于降低MC-CDMA系统中的干扰。该构造不同于基于布尔函数的方法，采用伽罗瓦域GF($p^{r}$)上的加法特征（其中$p$为素数，$r$为正整数）。首先，我们构建了长度为$p^{r}$的CCC，进而扩展构造了长度和大小均为$np^{r}$（$n$为任意正整数）的ZCCS，这些长度和大小此前未见报道。该方法的通用性进一步体现为：先前研究中报道的ZCCS长度均可作为特例包含其中，充分彰显了本方法的全面性与优越性。