  Most large-scale storage systems employ erasure coding to provide resilience
against disk failures. Recent work has shown that tuning this redundancy to
changes in disk failure rates leads to substantial storage savings. This
process requires code conversion, wherein data encoded using an
$[n^{I\mskip-2mu},k^{I\mskip-2mu}]$ initial code has to be transformed into
data encoded using an $[n^{F\mskip-2mu},k^{F\mskip-2mu}]$ final code, a
resource-intensive operation. Convertible codes are a class of codes that
enable efficient code conversion while maintaining other desirable properties.
In this paper, we focus on the access cost of conversion (total number of code
symbols accessed in the conversion process) and on an important subclass of
conversions known as the merge regime (combining multiple initial codewords
into a single final codeword).
  In this setting, explicit constructions are known for systematic
access-optimal Maximum Distance Separable (MDS) convertible codes for all
parameters in the merge regime. However, the existing construction for a key
subset of these parameters, which makes use of Vandermonde parity matrices,
requires a large field size making it unsuitable for practical applications. In
this paper, we provide (1) sharper bounds on the minimum field size requirement
for such codes, and (2) explicit constructions for low field sizes for several
parameter ranges. In doing so, we provide a proof of super-regularity of
specially designed classes of Vandermonde matrices that could be of independent
interest.
