Papers for

cryptography designers

Papers whose findings have a practical use for this group, as judged from the abstract. Open a paper to read what it means in practice.

Geometric insights reveal density limits of rank metric codes

A geometric approach to the density of rank-metric codes

Abstract: We study the asymptotic density of $\mathbb{F}_q$-point-free linear sections of geometrically irreducible projective varieties over finite fields. We then apply these results to rank-metric codes via determinantal varieties. Our approach recovers the known cases in which the density tends to $0$ or $1$ and determines the limit in the cases where it was previously unknown. To compute these previously unknown limits, we extend the notion of quasireflexivity to higher-dimensional varieties and show that determinantal varieties satisfy this property. This allows us to invoke the Chebotarev density theorem for varieties over finite fields to obtain the desired estimate.

Fri 18 SeptInformation Theory

The gist

Some codes used to protect data have a special property called rank metric that helps detect and correct errors. This paper looks at how often certain mathematical structures related to these codes appear over large finite fields. By using new geometric ideas and advanced number theory, the authors find exact values for these frequencies that were not known before. This helps understand which codes are common or rare, improving knowledge of their behavior at a large scale.

Open → 2609.21189v1