Improving spectral-based higher-order dual constructions

Determine whether suitable choices of the sign-capturing function and configuration in the spectral-based higher-order dual construction can produce an objective value that improves on the MRRW bound.

Background

The paper’s second construction uses a function that captures the sign of the valid region together with a configuration defining an eigenvalue-like object. The resulting higher-order dual solutions match the MRRW bound up to lower-order terms for balanced linear codes.

The construction has degrees of freedom in both the choice of the function and the choice of configuration. The paper explicitly leaves open whether exploiting these choices more effectively can yield a strict improvement over MRRW.