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Two-dimensional scan design with a linear test pattern generator is a practical built-in self-test technique, but it suffers from linear dependencies, which reduce the fault coverage. To alleviate this problem, networks of xor gates known as phase shifters can be employed. Current techniques based on the empirical criterion of imposing large phase shift differences (channel separations) between successive scan chains cannot adequately remove the dependencies. In this paper, we present a method that addresses explicitly the minimization of linear dependencies through appropriate selection of phase shift values. The method is based on the criterion of minimizing the linear dependencies in each cone of the circuit under test, and is applicable to any type of linear test pattern generator, be it linear feedback shift register of the external- xor or internal-xor type, cellular automaton, etc. Experimental results demonstrate the effect of the approach in increasing fault coverage.