  In this paper, we consider the convertible codes with the maximum distance
separable (MDS) property, which can adjust the code rate according to the
failure rates of devices. We first extend the notion of convertible codes to
allow initial and final codes with different parameters. Then, we investigate
the relationship between these parameters and thus establish new lower bounds
on the access cost in the merge and split regimes. To gain a deeper
understanding of access-optimal MDS convertible codes in the merge regime, we
characterize them from the perspective of parity check matrices. Consequently,
we present a necessary and sufficient condition for the access-optimal MDS
convertible code in the merge regime. Finally, as an application of our
characterization, we construct MDS convertible codes in the merge regime with
optimal access cost based on the extended generalized Reed-Solomon codes.
