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A new test-decompression methodology using a variable-rank multiple-polynomial linear feedback shift register (MP-LFSR) is proposed. In the proposed reseeding scheme, a test cube with a large number of specified bits is encoded with a high-rank polynomial, while a test cube with a small number of specified bits is encoded with a low-rank polynomial. Therefore, according to the number of specified bits in each test cube, the size of the encoded data can be optimally reduced. A variable-rank MP-LFSR can be implemented with a slight modification of a conventional MP-LFSR. The experimental results on the largest ISCAS'89 benchmark circuits show that the proposed methodology can provide much better encoding efficiency than the previous methods with adequate hardware overhead.