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Linear residue codes are useful for error control in both arithmetic operations and data transmission. When used in data transmission, they do not require special coding equipment, as encoding and decoding operations may be easily carried out in digital computers. In this paper, number-theoretic concepts are used to construct linear residue codes for the correction of burst errors. A general theory is developed for the class of codes derived from the multiplicative group modulo , an odd integer, which consists of all the integers smaller than and relatively prime to . Construction schemes for various classes of burst-error-correcting binary linear residue codes are determined and discussed.