On the number of multiplications necessary to compute a length-2nDFT

The number of multiplications necessary and sufficient to compute a length-2
ⁿ
DFT is determined. The method of derivation is shown to apply to the multiplicative complexity results of Winograd for a length-p
ⁿ
DFT, for p an odd prime number. The multiplicative complexity of the one-dimensional DFT is summarized for many possible lengths.