In this paper Barnes-Wall lattices for the K-user symmetric interference channel are considered. This paper is inspired by the work of Jafar [1], where a deterministic model is used in order to build a scheme to obtain the generalized degrees of freedom for each type of interference. The scheme uses a base Q expression to build the transmitted signals. This is an inspiration for [2] where, for some particularly chosen examples, Barnes-Wall lattices are used due to their multilevel structure to mimic the scheme proposed by Jafar and it is shown that it is possible to improve the performance. Following these ideas, here, a general method to select the Barnes-Wall lattice is provided for each type of interference according to the parameters given by the scheme proposed by Jafar. The case for any number of users is analysed and a rule is provided to determine how many users can be allocated with this method, related to the parameters given by Jafar, but using Barnes-Wall lattices.