Integer codes correcting/detecting burst errors within one byte and detecting burst errors within two bytes

This paper presents two classes of integer codes that are suitable for use in local area networks. The first class of codes can correct h-bit burst errors within one b-bit byte and detect l-bit burst errors within one b-bit byte (1 ≤ h < l < b), while the second class of codes, in addition to correcting/detecting the mentioned types of errors, can also detect d-bit burst errors within two b-bit bytes (1 ≤ d < b). Both classes of codes are defined over integer rings and are generated by computer search. To evaluate the performance of both classes of codes, we analyze their probabilities of incorrect decoding for binary symmetric and bursty channel.