# 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