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We consider the problem of characterizing the minimum average delay, or equivalently the minimum average queue length, of message symbols randomly arriving to the transmitter queue of a point-to-point link which dynamically selects a (n, k) block code from a given collection. The system is modeled by a discrete time queue with an IID batch arrival process and batch service. We obtain a lower bound on the minimum average queue length, which is the optimal value for a linear program, using only the mean (λ) and variance (σ2) of the batch arrivals. For a finite collection of (n, k) codes the minimum achievable average queue length is shown to be Θ(1/ε) as ε ↓ 0 where ε is the difference between the maximum code rate and λ. We obtain a sufficient condition for code rate selection policies to achieve this optimal growth rate. A simple family of policies that use only one block code each as well as two other heuristic policies are shown to be weakly optimal in the sense of achieving the 1/ε growth rate. An appropriate selection from the family of policies that use only one block code each is also shown to achieve the optimal coefficient σ2/2 of the 1/ε growth rate. We compare the performance of the heuristic policies with the minimum achievable average queue length and the lower bound numerically. For a countable collection of (n, k) codes, the optimal average queue length is shown to be Ω(1/ε). We illustrate the selectivity among policies of the growth rate optimality criterion for both finite and countable collections of (n, k) block codes.