A note about the traceability properties of linear codes

Authors:
Marcel Fernandez;Josep Cotrina;Miguel Soriano;Neus Domingo
Affiliations:
Technical University of Catalonia, Department of Telematic Engineering, Barcelona, Spain;Technical University of Catalonia, Department of Telematic Engineering, Barcelona, Spain;Technical University of Catalonia, Department of Telematic Engineering, Barcelona, Spain and Centre Tecnolgic de Telecomunicacions de Catalunya, Castelldefels, Barcelona, Spain;I.E.S. J.V Foix, Rubi, Barcelona, Spain
Venue:
ICISC'07 Proceedings of the 10th international conference on Information security and cryptology
Year:
2007

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Abstract

We characterize the traceability properties of linear codes. It is well known that any code of length n and minimum distance d is a c-TA code if c2 n/(n-d). In this paper, we show that a less restrictive condition can be derived. In other words, there exists a value ZC, with n - d ≤ ZC ≤ c(n - d), such that any linear code is c-TA if c ≤ n/ZC. We also prove that in many cases this condition is also necessary. These results are applied to cyclic and Reed-Solomon codes.