Using GF2 Matrices to Simplify Boolean Logic
Maurer, Peter M.
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Conventional logic simplification can be couched in terms of singular GF(2) matrices. The advantage to doing this is that different matrices can be used to combine terms that are separated by a Hamming distance greater than one. Although this sort of thing can be done without matrices, it is not clear what one would do after finding such terms. We show that by applying a matrix transformation to the inputs of a function, we can combine terms that are at arbitrary distances. We also show that we can further simplify functions by transforming the input vector space with a non-singular transformation.