Binary coding rate-versus-distance trade-off

Determine the asymptotically largest rate achievable by binary error-correcting codes of a prescribed relative minimum distance, thereby resolving the longstanding gap between the best-known upper and lower bounds.

Background

The paper identifies the rate-versus-distance trade-off for binary error-correcting codes as a longstanding problem. For each relative distance parameter, the asymptotic exponential growth rate of the largest code is not known, because the best upper bounds derived from Delsarte-type linear programming and the best existential lower bounds remain separated.

Although the paper develops higher-order Delsarte dual solutions, it does not determine the optimal rate-versus-distance function. The problem is therefore an unresolved external problem rather than a question answered by the paper.