Codes with burst distance and periodical burst errors

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 d(b) and then present a class of Maximum Distance Separable (MDS) codes (named as C-b code). In this paper, we derive an upper bound on d(b) for any linear code and a lower bound on d(b) for constant burst-b weight linear codes. We also present the existence of linear code with burst-b distance d(b) - 1 from code with burst distance d(b). 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 d(b) 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 d(b). Then, we do the same investigation for C-b and its dual code C-b(perpendicular to). Finally, we give decoding procedure for the code C-b in case of periodical burst errors. (C) 2022 Elsevier B.V. All rights reserved.