A low-rate improvement on the Elias bound (Corresp.)

An upper bound on the minimum distance of binary blocks codes, which is superior to Elias' bound for
R < 0.0509^+
, is obtained. The new hound has the same derivative
(-\infty)
at
R = 0
as Gilbert's lower bound. (Elias' bound has derivative
-\ln 2
at
R = 0)
.