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We investigate a practical approach to solving one instantiation of a distributed hypothesis testing problem under severe rate constraints that shows up in a wide variety of applications such as camera calibration, biometric authentication and video hashing: given two distributed continuous-valued random sources, determine if they satisfy a certain Euclidean distance criterion. We show a way to convert the problem from continuous-valued to binary-valued using binarized random projections and obtain rate savings by applying a linear syndrome code. In finding visual correspondences, our approach uses just 49% of the rate of scalar quantization to achieve the same level of retrieval performance. To perform video hashing, our approach requires only a hash rate of 0.0142 bpp to identify corresponding groups of pictures correctly.