Codes on s-periodic errors

Pankaj Kumar Das, Vinod Tyagi

Abstract


In this paper, we study linear codes capable of detecting and correcting s-periodic errors. Lower and upper bounds on the number of parity check digits required for codes detecting such errors are obtained. Another bound on codes correcting such errors is also obtained. An example of a code detecting such errors is provided.


Keywords


parity check matrix, syndromes, standard array, pe- riodic error.

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References


N. M. Abramson, A class of systematic codes for non-independent errors, IRE Trans. on Information Theory, IT-5, No. 4(1959), 150-157.

A. A. Alexander, R. M. Gryb and D. M. Nast, Capabilities of the tele-phone network for data transmission, Bell System Tech. J., Vol. 39, No. 3(1960), 431-476.

L. Berardi, B. K. Dass and R. Verma, On 2-repeated burst error de-tecting codes, Journal of Statistical Theory and Practice, Vol. 3, No. 2(2009), 381-391.

J. D. Bridwell and J. K. Wolf, Burst distance and multiple-burst correc-tion, Bell System Tech. J., Vol. 49(1970), 889-909.

R. T. Chien and D. T. Tang, On definitions of a burst, IBM Journal of Research and Development, Vol. 9, No. 4(1965), 292-293.

B. K. Dass and S. Madan, Repeated Burst Error Locating Linear Codes,

Discrete Mathematics, Algorithms and Applications, Vol. 2, No. 2(2010), 181-188.

B. K. Dass, and R. Verma, Repeated Burst Error Detecting Lin-ear Codes, Ratio Mathematica Journal of Applied Mathematics, Vol. 19(2009), 25-30.

P. Fire, A class of multiple-error-correcting binary codes for non-independent errors, Sylvania Report RSL-E-2, Sylvania Reconnaissance Systems Laboratory, Mountain View, Calif,(1959).

R. W. Hamming, Error-detecting and error-correcting codes, Bell Sys-tem Technical Journal, Vol. 29(1950), 147-160.

M. J. E. Golay, Notes on digital coding, Proc. IRE, Vol. 37(1949), 657.

M. J. E. Golay, Binary Coding, IRE Trans., PGIT-4(1954), 23-28.

R. C. Golay and D. K. Ray-Chaudhuri, On a class of Error Correcting Group Codes, Inf. and Control, Vol. 3(1960), 68-79.

R. C. Golay and D. K. Ray-Chaudhuri, Further Results on Error Cor-recting Binary Group Codes, Inf. and Control, Vol. 3(1960), 279-290.

A. Hocquenghem, Codes Corecteurs d’Erreurs, Chiffres, Vol. 2(1959), 147-156.

W. W. Peterson and E. J. Weldon(Jr.), Error-Correcting Codes, 2nd edition, The MIT Press, Mass, 1972.

S. H. Reiger, Codes for the correction of clustered errors, IRE Trans. Inform. Theory, IT-6(1960), 16-21.

G. E. Sacks, Multiple error correction by means of parity-checks, IRE Trans. Inform. Theory IT, 4(1958), 145 - 147.

B. D. Sharma, B. Rohtagi, Some Results on Weights of Vectors Having 2-Repeated Bursts, Cybernetics and Information Technologies, Vol. 11, No. 1(2011), 36-44.

J. J. Stone, Multiple burst error correction, Information and Control, Vol. 4(1961), 324-331.

V. Tyagi and P. K. Das, s-Alternate Error Correcting Linear Codes, J. of Combinatorics, Information & System Sciences, Vol. 35, No. 1-2(2010), 17-26.

www.themcdonalds.net/richard/index.php?title= Astrophotography Mounts: Periodic Error Correction.


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Copyright (c) 2012 Pankaj Kumar Das, Vinod Tyagi

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