The conjecture that no cyclic codes have both constant relative distance and dual distance

Let $q$ be a fixed prime power. An infinite family of cyclic codes over $\F_q$ has constant relative distance if its relative distance is bounded below by a positive constant, and has constant relative dual distance if the relative distance of the dual family is bounded below by a positive constant. Cyclic-code distance conjecture. There does not exist an infinite family of cyclic codes over $\F_q$ with both constant relative distance and constant relative dual distance. This is presented as an intermediate step toward the conjecture that asymptotically good cyclic codes do not exist; the paper gives no resolution.