Abstract:A longstanding open problem in coding theory is to determine the best (asymptotic) rate R 2 (δ) of binary codes with minimum constant (relative) distance δ. An existential lower bound was given by Gilbert and Varshamov in the 1950s. On the impossibility side, in the 1970s McEliece, Rodemich, Rumsey and Welch (MRRW) proved an upper bound by analyzing Delsarte's linear programs. To date these results remain the best known lower and upper bounds on R 2 (δ) with no improvement even for the important class of linea… Show more
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