In large-scale distributed storage systems, erasure coding is employed to ensure reliability against disk failures. Adapting code parameters to varying disk failure rates can lead to significant storage savings without compromising reliability. This motivates the design of convertible codes that enable efficient transformations between codes with different parameters. 

In this talk, I will focus on MDS convertible codes in the merge regime, i.e., merging multiple codewords from an initial MDS code into a single codeword of a final MDS code. Two key performance metrics for code conversions are access cost and bandwidth cost. I will present several low-field-size constructions that achieve optimal access cost. Notably, the field size requirement of one of these constructions matches the lower bound implied by the MDS conjecture in almost all cases. I will also briefly discuss a refinement that reduces the sub-packetization level of a previously known bandwidth-optimal construction.