Fix $n,k$ and pick a random generator polynomial $g(x)\in\Bbb F_q[x]$ of degree $n-k$ that divides $(x^n-1)$.
What is the average minimum distance $d_r$ of the cyclic code defined with this random $g(x)|(x^n-1)$?
What is the best minimum distance $d_b$ of the cyclic code defined with the best possible $g(x)$?
What is the best minimum distance $d_{opt}$ known among all possible $[n,k]_q$ codes?
How does $d_{opt}$ and $d_b$ and $d_r$ compare against one another?