Efficient encoding and message recovery for the constructed deletion-correcting code

Develop efficient encoding and message recovery algorithms for the constructed non-binary multiplicity-free deletion-correcting code based on set codes and stable-deletion-correcting permutation codes.

Background

The paper constructs a non-binary multiplicity-free code by combining a set code correcting deletions with a permutation code correcting stable deletions. It provides a decoding procedure under the assumption that suitable component decoders are available, but it does not provide efficient encoding and message recovery algorithms for the resulting code. The authors explicitly identify these algorithms as an important open problem.