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Communication networks conventionally operate with half-duplex methods and interference avoiding schemes to manage multiple transceivers. Here we consider a method in which nodes transmit and receive in concert to achieve full duplex communication without transmitter coordination. We build on a recent framework for full-duplex communication in ad-hoc wireless networks recently proposed by Zhang, Luo and Guo. An individual node in the wireless network either transmits or it listens to transmissions from other nodes but it cannot do both at the same time. There might be as many nodes as there are MAC addresses but we assume that only a small subset of nodes contribute to the superposition received at any given node in the network. We develop deterministic algebraic coding methods that allow simultaneous communication across the entire network. We call such codes choir codes. Users are assigned subspaces of F2m to define their transmit and listen times. Codewords on these subspaces are designed and proven to adhere to bounds on worst- case coherence and the associated matrix spectral norm. This in turn provides guarantees for multi-user detection using convex optimization. Further, we show that matrices for each receiver's listening times can be related by permutations, thus guaranteeing fairness between receivers. Compared with earlier work using random codes, our methods have significant improvements including reduced decoding/detection error and non-asymptotic results. Simulation results verify that, as a method to manage interference, our scheme has significant advantages over seeking to eliminate or align interference through extensive exchange of fine-grained channel state information.