  Let $K$ be an algebraically closed field with $Char K\neq 2$ and $(s_1, s_2,
\cdots, s_r)\in \mathbb{Z}^r$ a multicharge with $r>2$. Let $\mathcal {H}_n(q,
Q)$ be a cyclotomic Hecke algebra of type $G(r, 1, n)$, where $q\neq 0, 1$ and
$Q=(q^{s_1}, q^{s_2}, \cdots, q^{s_r})$. For each block $B$ of $\mathcal
{H}_n(q, Q)$, we introduce a new invariant, called block move vector, which can
be considered as a generalization of the weight $w(B)$. We prove by using block
move vector that block $B$ has finite representation type if and only if
$w(B)<2$, or $B$ is Morita equivalent to $K[x]/x^{w(B)+1}$. Blocks of finite
representation type with weight more than one are determined completely by
block move vectors. This result implies that some blocks of finite type are
Brauer tree algebras whose Brauer trees have exceptional vertex. We also
determine representation type for all the blocks of cyclotomic $q$-Schur
algebras. Moreover, by using our result, we construct examples of blocks with
the same weight that are not derived equivalent. Examples of derived equivalent
blocks being in different orbits under the adjoint action of the affine Weyl
group are also given.
