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Concurrent on-line testing (COLT) of many-core systems-on-chip (SoC) has been recently proposed by researchers in response to the growing threat of electronic wear-out to system operational lifetimes and to the increasing reliability and availability demands of safety-critical applications. Previous research in concurrent on-line testing has focused on centralized approaches to manage core testing while the system is available to execute normal user applications. However, as technology scaling allows dozens and hundreds of processing cores to be placed on a single chip, these centralized approaches are not scalable solutions. In this paper, a distributed concurrent on-line test scheduling protocol is proposed and evaluated against previously developed solutions. Our experiments show that a distributed COLT scheduler can test a moderately-sized SoC with a speedup of 3.85 over centralized approaches while consuming 84% less energy, and performance benefits improve as the number of cores per chip increases. This research also presents a core test ordering algorithm - Code-Division Core Test Scheduling - that provides an additional 40% reduction in system test latency compared to other schedulers.