CODES ON m-REPEATED SOLID BURST ERRORS

Abstract

In coding theory, several kinds of errors due to the different behaviours of communication channels have been considered and accordingly error detecting and error correcting codes have been constructed. In general communication due to the long messages, the strings of same type of error may repeat in a vector itself. The concept of repeated bursts is introduced by Beraradi, Dass and Verma [4] which has opened a new area of study. They defined 2-repeated bursts and obtained results for detection and correction of such type of errors. The study was further extended to m-repeated bursts [3]. Solid burst errors are common in many communications. This paper considers a new similar kind of error which will be termed as ‘m-repeated solid burst error of length b’. A lower bound on the number of parity checks required for the existence of codes that detect such errors is obtained. Further, codes capable of detecting and simultaneously correcting such errors have also been dealt with.

Keywords

• Parity check matrix,syndrome,standard array,solid burst error

References

1. [1] Arlat, J. and Carter, W. C.(1984), Implementation and Evaluation of a (b,k)-Adjacent Error- Correcting/Detecting Scheme for Supercomputer Systems, IBM J. Res. Develop. 28(2), 159-169.
2. [2] Das, P. K.(2013), On 2-repeated solid burst errors, International Journal in Foundations of Computer Science & Technology, 3(3), 41-47.
3. [3] Dass, B. K. and Verma, R.(2009), Repeated Burst Error Detecting Linear Codes, Ratio Mathematica - Journal of Applied Mathematics, 19, 25-30.
4. [4] Dass, B. K., Verma, R. and Berardi, L.(2009), On 2-Repeated Burst Error Detecting Codes, Journal of Statistical Theory and Practice, 3, 381-391.
5. [5] Fire, P.(1959), A Class of Multiple-Error-Correcting Binary Codes for Non-Independent Errors, Sylvania Report RSL-E-2, Sylvania Reconnaissance System Laboratory, Mountain View, Calif.
6. [6] Jensen, D. W.(2003), Block code to efficiently correct adjacent data and/or check bit errors, Patent number: US 6604222 B1, Date of Patent Aug 5,(www.google.com/patents/US6604222).
7. [7] Peterson, W.W. and Weldon(Jr.), E. J.(1972), Error-Correcting Codes, 2nd edition, The MIT Press, Mass.
8. [8] Reiger, S. H.(1960), Codes for the Correction of Clustered Errors, IRE Trans. Inform. Theory, IT-6, 16-21.

9. [9] Schillinger, A. G.(1964), A class of solid burst error correcting codes, Polytechnic Institute of Brooklyn , N.Y., Research Rept. PIBMRI, April, 1223-64.
10. [10] Sharma, B. D. and Dass, B. K.(1977), Adjacent error correcting binary perfect codes, J. Cybernetics, 7, 9-13.
11. [11] Sharma, B. D. and Rohtagi, B.(2011), Some Results on Weights of Vectors Having 2-Repeated Bursts, Cybernetics and Information Technologies, 11(1), pp. 36-44.
12. [12] Shiva, S. G. S. and Sheng, C. L.(1969), Multiple solid burst-error-correcting binary codes. IEEE Trans. Inform. Theory, IT-15, 188-189.