The conjecture that asymptotically good cyclic codes do not exist

Let $q$ be a fixed prime power. A family of cyclic codes over $\F_q$ is asymptotically good if it has positive limiting rate and positive limiting relative distance. Cyclic-code asymptotic-goodness conjecture. There does not exist an infinite family of asymptotically good cyclic codes over $\F_q$. The paper recalls this as a conjecture underlying limitations for cyclic-code-based double-circulant and Wozencraft codes, and does not resolve it.