Repeated Burst Error Locating Linear Codes

Abstract

This paper deals with derivation of bounds for linear codes that are able to detect and locate errors which occur during the process of transmission. The kind of errors considered are known as repeated burst errors. An illustration for such kind of a code has also been provided.

Repeated Burst Error Correcting Linear Codes

“…Thus, the total number of linear combinations that h j can not be equal to is the sum of linear combinations in (4) and (8). At worst, all these combinations might yield a distinct sum.…”

“…Further, these results were extended to the codes correcting burst errors occurring within a subblock (refer Dass and Tyagi [5]). In our earlier paper [4] the authors obtained bounds over the number of parity-check digits required for codes detecting 2repeated and m-repeated bursts of length b or less occurring within a single subblock, the sub-block containing errors being identified. In this paper we extend our study to the correction of repeated bursts occurring within a sub-block.…”

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].…”

“…Repeated burst error was introduced by Berardi, Dass and Verma in [1] and its general form was introduced by Dass and Verma in [5]. 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].…”

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

“…With the appearance of the paper entitled "Error-Locating Codes-A New Concept in Error Control" by Wolf and Elspas [17], a new direction of research in coding theory has been opened up and many papers are written in this direction. Some of them may be mentioned as [1], [2], [4], [5], [12], [15], [16]. The paper [17] introduced the concept of error-locating codes (EL-codes)-which stands in between error detection and error correction concept.…”