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，尤其是在多载波码分多址（MC-CDMA）领域，迫切需要先进的码构造方法。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。本文提出了一种全新的完备互补码（CCC）和Z互补码集（ZCCS）构造方法，用于降低MC-CDMA系统中的干扰。与基于布尔函数的方法不同，所提出的构造采用伽罗华域GF($p^{r}$)上的加法特征，其中$p$为素数，$r$为正整数。首先，我们构造了长度为$p^{r}$的CCC，进而将其扩展为具有未报导长度和大小的ZCCS，其长度为$np^{r}$，其中$n$为任意正整数。该方法的通用性进一步体现在，它涵盖了以往研究中报导的ZCCS长度作为特例，充分彰显了该方法的全面性与优越性。