Explicit constant-list insdel codes with efficient decoding

Construct explicit insertion–deletion codes with constant list size and efficient encoding and decoding algorithms that attain rates comparable to the existential bounds established for fixed list sizes.

Background

The paper’s achievability results are existential: they establish the existence of binary insertion–deletion codes with fixed list size and specified rate guarantees through probabilistic sampling and the Lovász local lemma. These arguments do not provide explicit code constructions, efficient encoders, or efficient decoders.

The unresolved problem is therefore to replace the existential guarantees with explicit code families, together with efficient encoding and decoding algorithms, while preserving comparable rates and constant list-size guarantees. This is a concrete construction and algorithmic challenge distinct from improving the paper’s asymptotic counting bounds.