Existence of asymptotically good cyclic codes

Determine whether there exists an infinite family of cyclic codes over a fixed finite field that is asymptotically good; specifically, prove or disprove the existence of cyclic codes with both rate and relative minimum distance bounded away from zero as the blocklength tends to infinity.

Background

The paper situates its constructions within broader questions about cyclic codes. A central longstanding question in coding theory asks whether the class of cyclic codes contains asymptotically good families, i.e., sequences of cyclic codes with both rate and relative minimum distance bounded away from zero.

The authors reference this as a motivating open problem and provide new explicit cyclic and negacyclic code families with good parameters, but they do not settle the asymptotic goodness question.