Some new results on equivalency of collusion-secure properties for Reed-Solomon codes

Silverberg (IEEE Trans. Inform. Theory, 2003, 49, (5), pp. 1312-1318) proposed a question on the equivalence of identifiable parent property and traceability property for Reed-Solomon code family. Earlier studies on Silverberg´s problem motivate us to think of the stronger version of the question of equivalence of separation and traceability properties. Both, however, still remain open. In this study, the authors integrate all the previous works on this problem with an algebraic way, and present some new results. It is notable that the concept of subspace subcode of Reed-Solomon code, which was introduced in error-correcting code theory, provides an interesting prospect for the author´s topic.