  The construction of complementary sets (CSs) of sequences with different set
size and sequence length become important due to its practical application for
OFDM systems. Most of the constructions of CSs, based on generalized Boolean
functions (GBFs), are of length $2^\alpha$ ($\alpha$ is a natural number).
Recently some works have been reported on construction of CSs having lengths
non-power of two, i.e., in the form of $2^{m-1}+2^v$ ($m$ is natural number,
$0\leq v <m $), $N+1$ and $N+2$, where $N$ is a length for which $q$-ary
complementary pairs exist. In this paper, we propose a construction of CSs of
lengths $M+N$ for set size $4n$, using concatenation of CSs of lengths $M$ and
$N$, and set size $4n$, where $M$ and $N$ are lengths for which $q$-ary
complementary pairs exists. Also, we construct CSs of length $M+P$ for set size
$8n$ by concatenating CSs of lengths $M$ and $P$, and set size $8n$, where $M$
and $P$ are lengths for which $q$-ary complementary pairs and complementary
sets of size $4$ exists, respectively. The proposed constructions cover all the
previous constructions as special cases in terms of lengths and lead to more
CSs of new sequence lengths which have not been reported before.
