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A test response compaction and diagnosis technique based on BCH error correction code is presented. Traditional time-domain BCH compaction is not very useful in practice because the area overhead is too large. On the other hand, space-domain BCH compaction does not have a sufficient compression ratio to support a multiple error diagnosis. The proposed time-space compaction technique shares the polynomials among scan chains to reduce the area overhead A Boolean satisfiability optimiser is employed to diagnose the minimum number of errors. In addition, an analytical model is proposed to estimate the aliasing probability, which helps to determine key parameters of the proposed compactor. To diagnose ten errors in a design of 500 k flip-flops, the compression ratio is more than 2600 and the area overhead is <5 of flip-flops.