Implementation of linear maps with circulant matrices via modulo 2 rectifier circuits of bounded depth
Abstract
In the present note we show that for any positive integer k an arbitrary Boolean circulant matrix can be implemented via modulo 2 rectifier circuit of depth 2k-1 and complexity O(n1+1/k), and also via circuit of depth 2k and complexity O(n1+1/k log-1/k n).
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