Abstract
AbstractArithmetic an codes are useful for detecting and correcting errors in arithmetic operations and digital data transmission. Especially, cyclic an codes are considered to be useful. First, outlines of binary cyclic an codes and burst errors are described. Second, a method to construct the binary cyclic an codes consisting of 2m ‐ 1 codewords is presented and the burst error correcting ability of these codes is discussed. the number of codewords generally is one of the most important parameters for selecting a suitable code for a given system. From these codes, a binary cyclic an code satisfying requirements of both the number of codewords and the correcting ability in the system can easily be chosen. A relation between the code rate and the correcting ability also is discussed. Finally, another relation between the burst error correcting ability and the random error correcting ability is discussed. As a result, using the constructing method proposed here, binary cyclic an codes can be constructed which will be useful not only for the burst error correction but also for the random error correction.
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