  We study recursive algorithm for computing DCT of lengths $N=q 2^m$ ($m,q \in
\mathbb{N}$, $q$ is odd) due to C.W.Kok. We show that this algorithm has the
same multiplicative complexity as theoretically achievable by the prime factor
decomposition, when $m \leqslant 2$. We also show that C.W.Kok's factorization
allows a simple conversion to a scaled form. We analyze complexity of such a
scaled factorization, and show that for some lengths it achieves lower
multiplicative complexity than one of known prime factor-based scaled
transforms.
