Abstract: There are several kinds of burst errors for which error detecting and error correcting codes have been constructed. In this paper, we consider a new kind of burst error which will be termed as ‘m-repeated burst error of length b(fixed)’. The paper presents lower bounds on the number of parity-check digits required for a linear code that is capable of detecting errors which are m-repeated burst errors of length b(fixed). Further, codes capable of detecting and simultaneously correcting such errors have also been studied.

Abstract: In [16], the author introduced a new pseudo-metric on the space Matm×s(Zq) which is the module space of all m × s matrices with entries from the finite ring Zq generalizing the classical Lee metric (see [17]) and the array RT- metric (see [19]) and named this pseudo-metric as the Generalized-Lee-RT-Pseudo-Metric (or the GLRTP-Metric). In this paper, we obtain some lower bounds for two dimensional array codes correcting burst errors (see [10]) with weight constraints under the GLRTP-metric.

Abstract: Lee weight is more appropriate for some practical situations than Hamming weight as it takes into account magnitude of each digit of the word. In this paper, we obtain a sufficient condition over the number of parity check digits for codes correcting random errors and simultaneously detecting burst errors with Lee weight consideration.

Abstract: A generalization of the Reiger bound is presented for the list decoding of burst errors. It is then shown that Reed-Solomon codes attain this bound.

Abstract: This paper introduces two channel models of correlated parallel channels. Then we analyze structure of error correcting codes over these correlated parallel channels. We derive necessary and sufficient conditions for these codes and some code construction is presented. We also show some upper and lower bounds on the coding rate of the error correcting codes for correlated parallel channels. The introduced channel models are related to burst error channels and the codes analyzed in this paper can be used as asymmetric interleaving codes for burst error channels.

Abstract: We give recursive constructions, valid for any field, of [n,k] codes capable of correcting a (wrap-around) burst of n - k erasures.

Abstract: Digital data stored in computers or transmitted over computer networks are constantly subject to error due to the physical medium in which they are stored or transmitted. Error-correction codes are means of introducing redundancy in the data so that even if part of it is corrupted or completely lost, the original data can be recovered. Error correcting codes are used in modern technology to protect information from errors. Burst error correcting codes are needed in virtually uncountable applications. Such codes will be called complete burst error correcting codes. There are quite a few constructions for complete burst error correcting codes. This paper presents an error correcting code based on the concept and the theory of the Latin Squares, where it employ the characteristics of the orthogonal Latin Squares to correct the errors. That is not complete burst error correcting codes, since it can correct most burst pattern of length i ≤ n, but not all of them. However, if the number of uncorrectable patterns is sufficiently small, this code can be used in practice as a burst error correcting code.

Abstract: Many kinds of errors in coding theory have been dealt with for which codes have been constructed to combat such errors. Though there is a long history concerning the growth of the subject and many of the codes developed have found applications in numerous areas of practical interest, one of the areas of practical importance in which a parallel growth of the subject took place is that of burst error detecting and correcting codes. The nature of burst errors differ from channel to channel depending upon the behaviour of channels or the kind of errors which occur during the process of data transmission. In very busy communication channels, errors repeat themselves more frequently. In view of this, it is desirable to consider repeated burst errors. The paper presents lower and upper bounds on the number of parity-check digits required for a linear code correcting errors in the form of repeated bursts. An upper bound for a code that detects m-repeated bursts has also been derived. Illustrations of several codes that correct 2-repeated bursts of different lengths have also been given.