通过伽罗瓦域上的加性特征构造CCC和ZCCS
Construction of CCC and ZCCS Through Additive Characters Over Galois Field
AI总结：
针对MC-CDMA系统中传统码构造方法码长灵活性不足的问题，提出利用伽罗瓦域GF($p^r$)上的加性特征构造CCC和ZCCS的新方法，可生成更多长度规模的码集且涵盖已有结果。
摘要：
随着无线通信技术，尤其是多载波码分多址（MC-CDMA）的快速发展，亟需先进的码构造方法。传统方法主要基于广义布尔函数，在码长灵活性方面存在局限。本文提出一种构造完全互补码（complete complementary codes，CCC）和Z互补码集（Z-complementary code sets，ZCCS）的新方法，用于降低MC-CDMA系统中的干扰。该构造方法与基于布尔函数的方法不同，采用伽罗瓦域GF($p^{r}$)上的加性特征，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，随后将其扩展以构造长度和规模均为$np^{r}$的ZCCS，其中$n$为任意正整数，这些长度此前未见报道。该方法的灵活性进一步体现在，它将已有研究中报道的ZCCS长度作为特殊情况包含在内，凸显了该方法的全面性与优越性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
