  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.
