Gilbert and Varshamov Meet Johnson - List Decoding Nearly-Optimal Binary Codes

Explore a groundbreaking lecture on list decoding nearly-optimal binary codes, presented by Silas Richelson from UC Riverside. Delve into the advancements in error-correcting code theory, focusing on Ta-Shma's breakthrough construction of an almost optimal binary code. Examine the improvements made to list-decoding algorithms, comparing the work of Alev et al. with the presenter's enhanced analysis. Discover how the new algorithm achieves list-decoding up to the Johnson bound for Ta-Shma's original code, recovering from a (1-ρ)/2-fraction of errors as long as ρ≥√ε. Gain insights into the intersection of Gilbert-Varshamov and Johnson bounds in the context of error-correcting codes during this 39-minute talk from the Simons Institute's series on Advances in the Theory of Error-Correcting Codes.