Codes detecting, locating and correcting random errors occurring in multiple sub-blocks

Abstract

In this paper, we study bounds on the number of check digits of linear codes that can detect multiple sub-blocks each affected by e or less random errors and can locate such corrupted multiple sub-blocks. Further, we obtain an upper bound on the number of check digits of linear codes which can correct such errors occurring in multiple subblocks. We also give examples of such codes. Subjclass [2010]. 94B05, 94B65.

Bounds on linear codes capable of detecting, locating and correcting of repeated burst errors prevailing in multiple sub-blocks

“…This helps to make a balance in the efficiency of the channel. Many papers are written in this direction, e.g., [2,3,4,8,12].…”

“…In paper [2], Das obtains bounds for linear code which can locate burst errors affecting more than one sub-block, whereas the paper [3] presents random error detecting, locating and correcting codes where errors are affecting multiple sub-blocks. In continuation with this direction of work, we plan to work for repeated burst error affecting multiple sub-blocks.…”

“…Repeated burst error affecting only single sub-block is studied by Dass and Madan in [7,8] where they obtain bounds for linear code correcting and locating such errors. In this correspondence, we study the situation when repeated burst errors are occurred in multiple sub-blocks and present bounds for linear codes which can detect, locate, also correct such errors, a parallel to the work done in [3]. Now, we take the definitions of different types of errors that we are going to study in this paper.…”