The multivariate merit factor of a Boolean function

A new metric, the multivariate merit factor (MMF) of a Boolean function, is presented, and various infinite recursive quadratic sequence constructions are given for which both univariate and multivariate merit factors can be computed exactly. In some cases these constructions lead to merit factors with non-vanishing asymptotes. A formula for the average value of 1/MMF is derived and a characterisation of the MMF in terms of cryptographic differentials is discussed.