Constructions bridging intermediate fragment-thickness regimes

Develop hybrid single-fragment forensic coding constructions that bridge the thick-fragment regime h=Theta(M^{1/d}), where periodic lifting is effective, and thinner-fragment regimes handled by discrepancy-based constructions, with the aim of combining their respective rate and explicitness properties.

Background

The paper’s periodic-lifting method provides explicit, high-rate constructions when the guaranteed fragment thickness is on the order of M{1/d}. By contrast, discrepancy-based constructions from prior work address thinner fragments but provide weaker rate guarantees and, in some settings, lack comparable explicitness.

The authors identify the intermediate regime between these approaches as unresolved and propose hybrid constructions as the means of connecting the two parameter ranges.

References

The periodic lifting approach is most effective when $h=\Theta(M{1/d})$, whereas the discrepancy-based constructions of handle thinner fragments but offer weaker rate guarantees. Hybrid constructions bridging these two regimes remain for future work.

— Single-Fragment Forensic Coding via Multidimensional Cyclically Permutable Codes  (2609.24575 - Sun et al., 21 Sep 2026) in Section 6, Conclusion and Open Problems