Linear residue codes are useful in a number of applications due to their ease of implementation. For error control in data transmission they do not require special equipment an encoding and decoding operations . can easily be carried out in digital computers. They are also useful for checking arithmetic operations in a computer.nIn this study an iterative procedure is used to construct linear residue codes tor the correction and detection of multiple random errors. this procedure and number-theoretic concepts are used Co develop a theory for a class of multiple error correcting codes which have the property that the number of code words is s prize number. Applications to the practical coding problem are also discussed and examples given.
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