Arithmetic Error Detecting Codes for Communications Links Involving Computers

Cyclic codes have been extensively studied for burst error detection. These codes involve modulo two algebra and are implemented by shift registers. Arithmetic-burst-error detecting codes are presented here which are easily implemented by standard arithmetic computer instructions. Unlike cyclic codes that have a probability of undetected error bursts independent of the burst length and polynomial generator, the probability of undetected burst errors varies with the code generator and the burst length. However, it is conjectured that the fraction of undetected error bursts is of the same order as that for cyclic codes. This is proved for asymmetric channels. Single, double, triple, and double burst error-detecting arithmetic codes are constructed.