Codes on m-repeated solid burst errors

Abstract

In coding theory, several kinds of errors due to the different behaviours of communication channels have been considered and accordingly error detecting and error correcting codes have been constructed. In general communication due to the long messages, the strings of same type of error may repeat in a vector itself. The concept of repeated bursts is introduced by Beraradi, Dass and Verma [4] which has opened a new area of study. They defined 2-repeated bursts and obtained results for detection and correction of such type of errors. The study was further extended to m-repeated bursts [3]. Solid burst errors are common in many communications. This paper considers a new similar kind of error which will be termed as ‘m-repeated solid burst error of length b’. A lower bound on the number of parity checks required for the existence of codes that detect such errors is obtained. Further, codes capable of detecting and simultaneously correcting such errors have also been dealt with.