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The structure of a uniform convolutional code, i.e., a code whose average distance is equal to its minimum distance, is examined, and results in a parity equation lattice. From this lattice, punctured uniform codes, i.e., uniform codes with parity bits deleted, are constructed, which can be threshold decoded and have limited error propagation. An "optimum" deletion sequence is provided. Some of the punctured uniform codes are optimal from a minimum-distance view point.