A Study of the Separating Property in Reed-Solomon Codes by Bounding the Minimum Distance

TL;DR

This paper investigates the separating property of Reed-Solomon codes by establishing minimum distance thresholds below which these codes lack the separating property, advancing understanding of their tracing capabilities.

Contribution

It provides new bounds on the minimum distance of Reed-Solomon codes that determine when they lose the separating property, addressing a question about their tracing capabilities.

Findings

Reed-Solomon codes do not possess the separating property below certain minimum distance thresholds.

The paper establishes specific minimum distance bounds related to the separating property.

Progress is made in understanding the tracing capabilities of Reed-Solomon codes under different conditions.

Abstract

According to their strength, the tracing properties of a code can be categorized as frameproof, separating, IPP and TA. It is known that if the minimum distance of the code is larger than a certain threshold then the TA property implies the rest. Silverberg et al. ask if there is some kind of tracing capability left when the minimum distance falls below the threshold. Under different assumptions, several papers have given a negative answer to the question. In this paper further progress is made. We establish values of the minimum distance for which Reed-Solomon codes do not posses the separating property.