In this paper we consider functions $F : {\mathbb F}^{m}_{2} \rightarrow {\{\pm\}}$ which satisfy certain linear and differential properties. The investigation of these properties is motivated by applications in cryptography. The linear property that we are interested in is “correlation immunity”, the differential properties are known under the name of “avalanche criteria”. It is not our purpose to construct new correlation immune functions or new functions with good differential properties, but we will describe known constructions (Maiorana-McFarland construction) and its variations in terms of group rings. This is (notationally) a quite useful description since it yields immediate further generalizations and it gives easy ways to obtain bounds on the maximum nonlinearity of the functions.