Existence theorems for transforms over finite rings with applications to 2-D convolution
David P. Maher · Mathematics of Computation · 1980
An existence theorem for Fourier-like transforms over arbitrary finite commutative rings is proven in a simple fashion. Corollaries for the case of residue class rings over the integers and extensions of those rings follow directly. The theory is applied to construct very fast algorithms for the computation of two-dimensional convolutions over the integers mod M \bmod \, M .