Code rates

The plots below give the points (d/n,k/n) where k, n run through the interval for which tables are available, and d is the minimum distance of the best code with word length n and dimension k known.

Trivial codes have k=n and d=1, or d=n and k=1.

The green line is the Gilbert-Varshamov asymptotic lower bound. We are guaranteed the existence of arbitrarily long codes above this bound.

The blue line is the Elias asymptotic upper bound: in the limit (with code length tending to infinity) codes with positive rate must remain below this. Other asymptotic bounds, such as the McEliece-Rodemich-Rumsey-Welch bound, are still slightly smaller.

q=2

q=3

q=4

q=5

q=7

q=8

q=9