Systems and methods for multi-user detection in a multiple access system are provided. In one aspect, an apparatus is provided. The apparatus comprises a processing unit configured to process received chips into received symbols for a plurality of users and a computation unit configured to compute a multi-user matrix using a Hadamard matrix, wherein the multi-user matrix relates user symbols for the plurality of users to the received symbols. The apparatus further comprises a detection unit configured to detect the user symbols for the plurality of users using the received symbols and the computed multi-user matrix.