The modified number theoretic transform over the direct sum of finite fields to compute the linear convolution

The modified number theoretic transform (MNTT) over the direct sum of finite fields is constructed. The MNTT application to computing linear convolution (LC) is discussed. The main advantage of the MNTT is the possibility of reducing computational complexity of an LC (in terms of numbers of arithmetical operations or computation time). However, using the MNTT decreases the dynamic range of the LC input.