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The -receiver Gaussian broadcast channel is a communication system in which a single codeword is transmitted over distinct Gaussian channels and is received by receivers. The receivers have no contact with each other and the channels have different signal-to-noise ratios. The purpose of this correspondence is to define the concept of group code for the -receiver Gaussian broadcast channel and study permutation codes as a special case. Such a code is generated by an initial vector , a group of orthogonal -by- matrices, and a sequence of subgroups of .