Democratic-type properties for secret sharing from Hermitian and norm-trace curves

Establish democratic-type properties—specifically the existence and systematic structure of maximal non-u-qualifying participant sets—for linear ramp secret sharing schemes constructed from codes associated with the Hermitian curve and, more generally, norm-trace curves.

Background

The work primarily analyzes monomial‑Cartesian code-based constructions to achieve democratic properties, i.e., systematic maximal non‑u‑qualifying sets that provide a second security layer. Algebraic geometry codes from curves such as the Hermitian and norm‑trace curves are central in coding theory and secret sharing, offering strong parameters.

The open question invites transferring or adapting the democratic framework to these AG code families, seeking analogous systematic non‑qualifying set structures that would extend the second-layer security insights beyond monomial‑Cartesian settings.