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The version of record is available online at: http://dx.doi.org/10.1007/s10623-021-00988-z ; 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. ; This work has been supported by the Spanish Government Grant TCO-RISEBLOCK (PID2019-110224RB-I00) MINECO . ; Peer Reviewed ; Postprint (published version)

We introduce non-binary IPP set systems with traceability properties that have IPP codes and binary IPP set systems with traceability capabilities as particular cases. We prove an analogue of the Gilbert–Varshamov bound for such systems. ; Marcel Fernandez: The work of M. Fernández has been supported by the Spanish Government Grant TEC2015- 68734-R and Catalan Government Grant SGR 782. ; Peer Reviewed ; Postprint (author's final draft)