BURSTS/CT-BURSTS DETECTED BY b-SBEC CODES AND SOLID BURSTS UNDETECTED BY CYCLIC CODES

Yıl 2014, Cilt: 2 Sayı: 2, 1 - 9, 01.12.2014

PANKAJ KUMAR Das

https://doi.org/10.36753/mathenot.207618

Öz

In coding theory, several kinds of errors which depend on thenature of the communication channel are to be dealt with and accordinglycodes are constructed to detect and correct such errors. Burst, CT-burst andsolid burst errors are common in many communication channels. Differenttypes of linear codes have been developed to deal with such errors.also quite possible that in communication more than one type of error occursimultaneously. The code which is developed to deal with one type of errormay or may not be able to deal with the other type of error.The paper presents the minimum number of burst/CT-burst errors that willbe detected by a b-SBEC code. A lower bound on parity check digits for suchcode is obtained. Further, the paper presents the number of solid burst errorsthat will be gone detected/undetected by a cyclic code. By a b-SBEC code,we mean a linear code that corrects all solid bursts of length b or less

Anahtar Kelimeler

Parity check digit, burst, CT-burst, solid burst, cyclic codes

Kaynakça

• Abramson, N.M., A class of systematic codes for non-independent errors. IRE Trans. on Information Theory, IT-5 (1959), no. 4, 150-157.
• Arlat, J. and Carter, W.C., Implementation and Evaluation of a (b, k)-Adjacent Error- Cor- recting/Detecting Scheme for Supercomputer Systems. IBM Journal of Research and Devel- opment 28 (1984), no. 2, 159-169 .
• Alexander, A.A., Gryb, R.M. and Nast, D.M., Capabilities of the telephone network for data transmission. Bell System Tech. J., 39 (1960), no. 3, 431-476 .
• Argyrides, C.A., Reviriego, P., Pradhan, D.K. and Maestro, J.A., Matrix-Based Codes for Adjacent Error Correction. IEEE Transactions on Nuclear Science, 57 (2010), no. 4, 2106- 2111 .
• Bossen, D.C., b-Adjacent Error Correction. IBM Journal of Research and Development, 14 (1970), no. 4, 402-408.
• Bridwell, J.D. and Wolf, J.K., Burst distance and multiple-burst correction. Bell System Tech. J., 49 (1970), 889-909.
• Chien, R.T. and Tang, D.T., On definitions of a burst. IBM Journal of Research and Devel- opment, 9 (1965), no. 4, 292-293.
• Das, P.K., Codes Detecting and Correcting Solid Burst Errors. Bulletin of Electrical Engi- neering and Informatics, 1 (2012), no. 3, 225-232.
• Das, P.K., Codes Detecting and Locating Solid Burst Errors. Romanian Journal of Mathe- matics and Computer Science. 2 (2012), no. 2, 1-10.
• Das, P.K., Blockwise Solid Burst Error Correcting Codes. International Journal on Informa- tion Theory, 1 (2012), no. 1, 11-17.
• Das, P.K., On 2-Repeated Solid Burst Errors, International Journal in Foundations of Com- puter Science & Technology, 3 (2013), no. 3, 41-47.
• Das, P.K., Codes on m-repeated solid burst errors, TWMS J. App. Eng. Math., 3 (2013), no. 2, 142-146.
• Etzion, T., Optimal codes for correcting single errors and detecting adjacent errors. IEEE Trans. Inform. Theory, 38 (1992), 1357-1360.
• Fire, P., A class of multiple-error-correcting binary codes for non-independent errors, Syl- vania Report RSL-E-2, Sylvania Reconnaissance Systems Laboratory, Mountain View, Calif, (1959).
• Hamming, R.W., Error-detecting and error-correcting codes. Bell System Technical Journal, 29 (1950), 147-160.
• Jain, S., Moderate density open-loop burst error detection for cyclic codes. Tamsui Oxford Journal of Mathematical Science, 18 (2002), no. 1, 17-29.
• Jensen, D.W., Block code to efficiently correct adjacent data and/or check bit errors. Patent no: US 6604222 B1. Date of Patent Aug 5(www.google.com/patents/US6604222). (2003).
• Peterson, W.W. and Weldon(Jr.), E.J., Error-Correcting Codes. 2nd edition, The MIT Press, Mass, (1972).
• Prange, E., Cyclic Error-correcting Codes in Two Symbols. U.S. Air Force Cambridge Re- search Centre, AFCRC-TN-57-103, Bedford, Massachusetts, (1957).
• Reiger, S. H., Codes for the Correction of Clustered Errors, IRE Trans. Inform. Theory, IT-6 (1960), 16-21.
• Schillinger, A.G., A class of solid burst error correcting codes. Polytechnic Institute of Brook- lyn, N.Y., Research Rept. PIBMRI. 1223-64, April (1964).
• Siap, I., Burst error enumeration of m-array codes over rings and its applications. Eur. J. Pure Appl. Math., 3 (2010), no. 4, 653-669.
• Siap, I., CT burst error weight enumerator of array codes. Albanian J. Math., 2 (2008), no. 3, 171- 178.
• Sharma, B.D. and Dass, B.K., Adjacent error correcting binary perfect codes. J. Cybernetics, 7 (1977), 9-13.
• Sharma, B.D. and Rohtagi, B., Moderate-density 2-repeated burst error detecting cyclic codes. International Journal of Emerging trends in Engineering and Development, 4 (2012), no. 2, 49-55.
• Shiva, S.G.S. and Sheng, C.L., Multiple solid burst-error-correcting binary codes. IEEE Trans. Inform. Theory, IT-15 (1969), 188-189.
• Stone, J.J., Multiple burst error correction. Information and Control, 4 (1961), 324-331.
• Temiz, F. and Siap, V., Linear block and array codes correcting repeated CT-burst errors, Albanian Journal of Mathematics, 7 (2013), no. 2, 77-92.
• Department of Mathematics, Shivaji College (University of Delhi), Raja Garden, New Delhi - 110 027, India
• E-mail address: [e-mail]