The output space of a linear decompressor must be sufficiently large to contain all the test cubes in the test set. The idea proposed in this paper is to use scan inversion to transform the output space of a linear decompressor so as to reduce the number of inputs required thereby increasing the encoding efficiency while still keeping all the test cubes in the output space. Any existing method for designing a linear decompressor (either combinational or sequential) can be used first to obtain the best linear decompressor that it can. Using that linear decompressor as a starting point, the proposed method improves the encoding efficiency further. The key property used by the proposed method is that scan inversion is a linear transformation of the output space and thus the output space remains a linear subspace spanned by a Boolean matrix. Using this property, a systematic procedure based on linear algebra is described for selecting the set of inverting scan cells to maximize encoding efficiency. Experiments indicate that significant improvements in encoding efficiency can be achieved.