On the relationship between the traceability properties of Reed-Solomon codes

José Moreira; Marcel Fernández; Miguel Soriano

doi:10.3934/amc.2012.6.467

Article Contents

2012, Volume 6, Issue 4: 467-478. Doi: 10.3934/amc.2012.6.467

This issue Previous Article An algebraic approach for decoding spread codes Next Article Extended combinatorial constructions for peer-to-peer user-private information retrieval

On the relationship between the traceability properties of Reed-Solomon codes

1.
Department of Telematics Engineering, Universitat Politècnica de Catalunya, C. Jordi Girona 1-3, 08034 Barcelona
2.
Department of Telematics Engineering, Universitat Politècnica de Catalunya, C. Jordi Girona 1-3, 08034 Barcelona, Spain, and Centre Tecnològic de Telecomunicacions de Catalunya (CTTC), Av. Carl Friedrich Gauss 7, 08860 Castelldefels (Barcelona)

Received: September 30, 2011

Revised: May 31, 2012

Published: October 2012

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Abstract

Fingerprinting codes are used to prevent dishonest users (traitors) from redistributing digital contents. In this context, codes with the traceability (TA) property and codes with the identifiable parent property (IPP) allow the unambiguous identification of traitors. The existence conditions for IPP codes are less strict than those for TA codes. In contrast, IPP codes do not have an efficient decoding algorithm in the general case. Other codes that have been widely studied but possess weaker identification capabilities are separating codes. It is a well-known result that a TA code is an IPP code, and an IPP code is a separating code. The converse is in general false. However, it has been conjectured that for Reed-Solomon codes all three properties are equivalent. In this paper we investigate this equivalence, providing a positive answer when the number of traitors divides the size of the ground field.

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Mathematics Subject Classification: Primary: 94B60; Secondary: 94B65.

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