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Repeated burst error correcting linear codes. (English) Zbl 1178.94237

Summary: 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.

MSC:

94B20 Burst-correcting codes
94B65 Bounds on codes
94B25 Combinatorial codes
Full Text: DOI

References:

[1] Abramson N. M., IRE Trans. on Information Theory 5 pp 150– · doi:10.1109/TIT.1959.1057524
[2] Berardi L., Journal of Statistical Theory and Practice
[3] Bridwell J. D., Bell System Tech. J. 99 pp 889–
[4] DOI: 10.1147/rd.94.0292 · doi:10.1147/rd.94.0292
[5] Dass B. K., Ratio Mathematica – Journal of Applied Mathematics
[6] DOI: 10.1002/j.1538-7305.1950.tb00463.x · doi:10.1002/j.1538-7305.1950.tb00463.x
[7] Kasahara H., Electronics and Communications in Japan 50 pp 9–
[8] Liu C. L., Introduction to Combinatorial Mathematics (1968) · Zbl 0188.03801
[9] Peterson W. W., Error-Correcting Codes (1972) · Zbl 0251.94007
[10] Posner E. C., J. Soc. Indust. Appl. Math. 13
[11] Sacks G. E., IRE Trans. Inform. Theory 4 pp 145– · doi:10.1109/IRETIT.1958.6741947
[12] DOI: 10.1016/S0019-9958(61)80048-X · Zbl 0111.32402 · doi:10.1016/S0019-9958(61)80048-X
[13] Wolf J. K., IEEE Trans. On Information Theory 11 pp 281– · Zbl 0134.15301 · doi:10.1109/TIT.1965.1053771
[14] Wyner A. D., IEEE Transactions on Information Theory pp 124–
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