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Excessive switching activity during shift cycles in scan-based cores imposes considerable test power challenges. To ensure rapid and reliable test of SOCs, we propose a scan chain modification methodology that transforms the stimuli to be inserted to the scan chain through logic gate insertion between scan cells, reducing scan chain transitions. We introduce a novel matrix band algebra to formulate the impact of scan chain modifications on test stimuli transformations. Based on this analysis, we develop algorithms for transforming a set of test vectors into power-optimal test stimuli through cost-effective scan chain modifications. Experimental results show that scan-in power reductions exceeding 90% for test vectors and 99.5% for test cubes can be attained by the proposed methodology.