Strong explicitness of the AEL nearly-MDS construction

Determine whether the Alon–Edmonds–Luby (AEL) nearly-MDS code construction based on expander codes is strongly explicit, i.e., whether there exists an algorithm that, given row and column indices, outputs the corresponding generator-matrix entry in time polynomial in the bit-length of the indices for all block lengths.

Background

The AEL construction achieves nearly-MDS trade-offs over constant-sized alphabets using expander-code techniques defined via parity-check representations or layered systematic forms. The paper adopts a notion of strong explicitness where individual generator-matrix entries must be computable in polylogarithmic time in the block length.

While the authors provide strongly explicit constructions approaching the Singleton bound via their framework, they explicitly note they cannot verify strong explicitness for the AEL construction, leaving open whether AEL meets this stronger criterion.