Codes with burst distance and periodical burst errors

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Burst-b distance introduced by Wainberg and Wolf (1972) has been found to be useful for correction of multiple burst errors and multiple erasures. Villalba et al. (2016) have derived extended Reiger and Singleton bound for linear code with minimum burst-b distance db and then present a class of Maximum Distance Separable (MDS) codes (named as Cb code).In this paper, we derive an upper bound on db for any linear code and a lower bound on db for constant burst-b weight linear codes. We also present the existence of linear code with burst-b distance db−1 from code with burst distance db. The cardinality of a linear code and the connection of linearly independent columns of the parity check matrix of any MDS code with the distance db are also given. Further, we consider periodical burst error which is found in many communication channels and investigate periodical burst-detection and -correction capability of linear codes having distance db. Then, we do the same investigation for Cb and its dual code Cb⊥. Finally, we give decoding procedure for the code Cb in case of periodical burst errors.