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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.

Genus Osteobrama Heckel is characterized by strongly compressed, fairly deep body with abdominal edge sharp and trenchant entirely or from the pelvic fin base to vent; anal fin long with 14-36 rays, of which 11-13 are branched rays. The fishes of this genus are distributed in Pakistan, India, Bangladesh, Burma, and Yunnan (China). Present study involve six Osteobrama species viz. O. belangeri, O. cotio, O. cunma, O. feae, O. serrata sp. nov., and O. vigorsii. Out of the 655 positions analyzed in the COI sequence dataset, 171 positions (26.1%) were variable, and 151 positions (23%) were parsimoniously informative. The genetic distance between Osteobrama species ranges from 7.10% (between O. cotio and O. serrata sp. nov.) to 22.86% (between O. belangeri and O. feae) for COI sequences and 3.04% (between O. serrata sp. nov. and O. cunma) to 9.89% (between O. serrata sp. nov. and O. belangeri) for 16S sequences. Osteobrama belangeri show very high interspecies K2P distance with all other Osteobrama species for COI and 16S datasets. Best fit models for COI and 16S rRNA dataset were HKY + G + I and K2 + G, respectively. The maximum-likelihood (ML) phylogenetic trees were constructed using the COI and 16S rRNA sequences.

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Abstract. The paper deals with repeated low-density burst error detecting codes with a specified weight or less. Linear codes capable of detecting such errors have been studied. Further codes capable of correcting and simultaneously detecting such errors have also been dealt with. The paper obtains lower and upper bounds on the number of parity-check digits required for such codes. An example of such a code has also been provided.