Improve alphabet size below exp(~Theta(1/η^4)) for quasi-linear nearly-MDS codes
Construct explicit nearly-MDS linear codes over constant-sized alphabets, encodable and erasure-decodable in quasi-linear time, whose alphabet size scales strictly better than exp(~Theta(1/η^4)) as the gap-to-capacity parameter η tends to 0.
References
Our work motivates and leaves open the question of explicit construction of nearly-MDS codes encodable and erasure-decodable in quasi-linear time that achieve an alphabet size better than \exp(\tilde{\Theta}(1/\eta4)) for gap to capacity \eta > 0.
— Optimal Erasure Codes and Codes on Graphs
(Chen et al., 3 Apr 2025) in Concluding Remarks