Cyclic convolution algorithms over finite fields: Multidimensional considerations

By making an example of the earlier proposed cyclic convolution algorithms, the computational efficiency of the multidimensional techniques over finite fields is investigated. It is shown that the multidimensional techniques are inferior to the directly designed algorithms for all lengths except when applied to lengths whose exponents are relatively prime. Relations between the complexities of the directly designed algorithms and those derived through the multidimensional techniques are also established in various cases.