2025/04/25 by Dinesen, Johan Vester, Byrne, Eimear, Freij-Hollanti, Ragnar +1
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2504.18294
The connection between secret sharing and matroid theory is well established. In this paper, we generalize the concepts of secret sharing and matroid ports to q-polymatroids. Specifically, we introduce the notion of an access structure on a vector space, and consider properties related to duality, minors, and the relationship to q-polymatroids. Finally, we show how rank-metric codes give rise to secret sharing schemes within this framework.