Strict improvement of the minimum-distance bound

Determine whether the lower bound in Theorem 1.1 for the minimum distance of generalized graph codes on ℓ-partite graphs can be improved strictly.

Background

Theorem 1.1 gives a spectral lower bound on the minimum distance of generalized graph codes on ℓ-partite graphs. The bound is derived using the second-largest adjacency eigenvalue of the underlying regular graph and the minimum distance of the component code.

The paper explicitly leaves unresolved whether this estimate is optimal or whether a strictly stronger universal lower bound can be established.