Proposed are methods and apparatuses for synthesis of a new class of compressors called augmented multimode compactors, capable of achieving a flexible trade-off between compaction ratio, observability, control data volume and diagnostic properties in the presence of a large number of unknown values. The augmented multimode compactors reduce and/or completely avoid the X-masking effect in the compacted test responses. In addition, a requirement for constructing compactors is that any single error in the test response produces a unique erroneous signature within S consecutive shift cycles where the erroneous signature is calculated as a difference between the faulty signature and the fault-free signature.