Number of multiplications necessary to compute length-2n two-dimensional discrete Hartley transform DHT (2n; 2)

The multiplicative complexity of the two-dimensional discrete Hartley transform (2D DHT) of size 2ⁿ*2ⁿ, where n is a positive integer, is determined. The method of deviation is based on linear congruences and a ring structure. The minimal number of real multiplications necessary to compute a length-2ⁿ two-dimensional discrete Hartley transform over the field Q of rational numbers is 2²ⁿ⁺¹1-6(n-1)2ⁿ-8. DHT (2ⁿ; 2) has the same multiplicative complexity as a corresponding real data 2D-DFT.