If binary codes existed that exceed Gilbert-Varshamov bound they could not reach the cutoff rate of BSC

Binary block codes exceeding the Gilbert-Varshamov bound on the minimum Hamming distance (if such codes exist) have their error exponents below the one of the binary symmetric channel (BSC) in the interval (R/sub crit/, R/sub c/) and they cannot reach the cutoff rate R/sub 0/ and thus the capacity R/sub c/ of the BSC if a maximum likelihood decoder (MLD) is used.