  This paper is focused on efficient design of complete complementary codes
(CCCs) which have found wide applications in coding, signal processing and
wireless communication due to their zero auto- and cross-correlation sum
properties. A major motivation of this research is that the existing
state-of-the-art can generate CCCs with certain lengths only and therefore may
not meet the diverse requirements in practice. We introduce a new tool called
multivariable functions and propose a direct construction of CCCs with any
\textit{arbitrary} lengths in the form $\prod_{i=1}^k p_i^{m_i}$, where $k$ is
a positive integer, $p_1,p_2,\hdots,p_k$ are prime numbers and
$m_1,m_2,\hdots,m_k$ are positive integers whose sum is not less than 1. For
$k=1$ and $p_1=2$, our proposed generator reduces to the exact
Golay-Davis-Jedwab (GDJ) sequence generator as a special case. For $k>1$ and
$p_1=p_2=\cdots=p_k=2$, it gives rise to the conventional CCCs with
power-of-two lengths which are obtained from generalized Boolean functions.
