BURST ERROR-CORRECTING BINARY CYCLIC AN CODES CONSISTING 2(M)-1 CODEWORDS

Arithmetic AN codes are useful for detecting and correcting errors in arithmetic operations and digital data transmission. Especially, cycli c AN Codes are considered to be useful. First, outlines of binary cycl ic AN codes and burst errors ate described. Second,a method to constru ct the binary cyclic AN codes consisting of 2(m)-1 codewords is presen ted and the burst error correcting ability of these codes is discussed . The number of codewords generally is one of the most important param eters for selecting a suitable code for a given system. From these cod es, a binary cyclic AN code satisfying requirements of both the number of codewords and the correcting ability in the system can easily be c hosen. A relation between the code rate and the correcting ability als o is discussed. Finally, another relation between the burst error corr ecting ability and the random error correcting ability is discussed. A s a result, using the constructing method proposed here, binary cyclic AN codes can be constructed which will be useful not only. for the bu rst error correction but also for the random error correction.