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.

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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.

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Barilius is an important genus of fish family Cyprinidae, which comprises 22 species from Indian region. This study aimed to characterize five commonly occurring Bariline species, for example, Barilius bakeri. Barilius gatensis. Barilius vagra. Barilius bendelisis and Barilius tileo, across the country using partial mitochondrial 16 S rRNA gene, to estimate the order of inter- and intra-species divergence among these species and to establish phylogenetic and evolutionary relationships. The average inter-specific divergence was estimated as 7.10%. Intra-specific divergence of 0.20% and 0.10% was observed in B. gatensis and B. bendelisis that exhibited three and two haplotypes with 0.70 and 0.60 haplotype diversities, respectively. The NJ and MP phylogenetic trees were constructed using 16 S rRNA sequences along with sequences of the other five Indian cyprinid species retrieved from NCBI. Phylogenetic trees revealed five discrete branches each as a distinct species of the genus and exhibited identical phylogenetic relationship with other cyprinids. The study provided adequate information to distinguish the five Barilius species and indicated the suitability of 16S rRNA gene sequences in genetic divergence and phylogenetic studies.

The mitochondrial control region has been the first choice for examining the population structure but hypervariability and homoplasy have reduced its suitability. We analysed eight populations using control region for examining the population structure of Hilsa. Although the control region analysis revealed broad structuring between the Arabian Sea and Bay of Bengal (F ST  0.0441, p < 0.001) it was unable to detect structure among riverine populations. These results suggest that the markers used must be able to distinguish populations and control region has led to an underestimation of genetic differentiation among populations of Hilsa.