  The complexity of a block of a symmetric algebra can be measured by the
notion of defect, a numerical datum associated with each of the simple modules
contained in the block. Geck showed that the defect is a block invariant for
Iwahori-Hecke algebras of finite Coxeter groups in the equal parameter case,
and speculated that a similar result should hold in the unequal parameter case.
We prove that the defect is a block invariant for all cyclotomic Hecke algebras
associated with the complex reflection groups of the infinite series
$G(l,p,n)$, which include the Weyl groups of type $B_n$ in the unequal
parameter case. In particular, for the groups $G(l,1,n)$, we show that the
defect corresponds to the notion of weight in the sense of Fayers. We thus also
obtain a new way of computing the weight, which uses a generalisation of the
notion of hook lengths. We further show computationally that the defect is a
block invariant for all cyclotomic Hecke algebras of exceptional type for which
the blocks are known, and we conjecture that the result should hold for all
complex reflection groups. Finally, we obtain that the defect is also a block
invariant for cyclotomic Yokonuma-Hecke algebras.
