Home Articles List Article Information
Transactions on Combinatorics
Journal Archive
Volume Volume 7 (2018)
Volume Volume 6 (2017)
Volume Volume 5 (2016)
Volume Volume 4 (2015)
Volume Volume 3 (2014)
Volume Volume 2 (2013)
Volume Volume 1 (2012)
Das, P. (2015). Linear codes on solid bursts and random errors. Transactions on Combinatorics, 4(2), 45-55. doi: 10.22108/toc.2015.6189
Pankaj Kumar Das. "Linear codes on solid bursts and random errors". Transactions on Combinatorics, 4, 2, 2015, 45-55. doi: 10.22108/toc.2015.6189
Das, P. (2015). 'Linear codes on solid bursts and random errors', Transactions on Combinatorics, 4(2), pp. 45-55. doi: 10.22108/toc.2015.6189
Das, P. Linear codes on solid bursts and random errors. Transactions on Combinatorics, 2015; 4(2): 45-55. doi: 10.22108/toc.2015.6189

Linear codes on solid bursts and random errors

Article 5, Volume 4, Issue 2, June 2015, Page 45-55  XML PDF (224 K)
Document Type: Research Paper
DOI: 10.22108/toc.2015.6189
Author
Pankaj Kumar Das
Shivaji College (University of Delhi)
Abstract
‎The paper presents lower and upper bounds on the number of parity check digits required for a linear code that detects solid bursts of length $b$ or less and simultaneously any $e$ or less random errors‎. ‎An example of such a code is also provided‎. ‎Further‎, ‎codes capable of detecting and simultaneously correcting such errors have also been dealt with‎.
Keywords
Parity check matrix; syndrome; solid burst error
Main Subjects
11T71 Algebraic coding theory; cryptography
References
C‎. ‎A‎. ‎Argyrides‎, ‎P‎. ‎Reviriego‎, ‎D‎. ‎K‎. ‎Pradhan and J‎. ‎A‎. ‎Maestro (2010). ‎Matrix-Based Codes for Adjacent Error Correction. IEEE T‎. ‎NUCL‎. ‎SCI.. 57 (4), 2106-2111
J‎. ‎Arlat and W‎. ‎C‎. ‎Carter (1984). ‎Implementation and Evaluation of a (b,k)-Adjacent Error-Correcting/Detecting Scheme for Supercomputer Systems. IBM J‎. ‎Res‎. ‎Develop.. 28 (2), 159-169
D‎. ‎C‎. ‎Bossen (1970). ‎$b$-Adjacent Error Correction. IBM J‎. ‎Res‎. ‎Develop.. 14 (4), 402-408
P‎. ‎K‎. ‎Das (2012). ‎Codes Detecting and Correcting Solid Burst Errors. Bulletin of Electrical Engineering and Informatics. 1 (3), 225-232
P‎. ‎K‎. ‎Das (2012). ‎Codes Detecting and Locating Solid Burst Errors. Rom‎. ‎J‎. ‎Math‎. ‎Comput‎. ‎Sci.. 2 (2), 1-10
P‎. ‎K‎. ‎Das (2012). ‎Blockwise Solid Burst Error Correcting Codes. International Journal on Information Theory. 1 (1), 11-17
P‎. ‎K‎. ‎Das (2013). ‎Codes correcting and simultaneously detecting solid burst errors. Com‎. ‎Eng‎. ‎App-Journal. 2 (1), 143-150
P‎. ‎K‎. ‎Das (2012). ‎(1,3) Optimal Linear Codes on Solid Bursts. International Journal of Information Security Science. 1 (4), 106-111
B‎. ‎K‎. ‎Dass and S‎. ‎K‎. ‎Muttoo (1980). ‎A bound for random and closed loop burst errors detecting codes. Inform‎. ‎Sci.. 20, 151-156
T‎. ‎Etzion (1992). ‎Optimal codes for correcting single errors and detecting adjacent errors. IEEE Trans‎. ‎Inform‎. ‎Theory. 38, 1357-1360
R‎. ‎W‎. ‎Hamming (1950). ‎Error-detecting and error-correcting codes. Bell System Tech‎. ‎J.. 29, 147-160
D‎. ‎W‎. ‎Jensen (2003). Block code to efficiently correct adjacent data and/or check bit errors. ‎Patent no‎: ‎US 6604222 B1‎, ‎Date of Patent Aug 5, http://www.google.com/patents/US6604222.
W‎ ‎.W.‎ ‎Peterson and E‎. ‎J‎. ‎Weldon(Jr.) (1972). Error-Correcting Codes. ‎Second edition‎, ‎The M‎. ‎I‎. ‎T‎. ‎Press‎, ‎Cambridge‎, ‎Mass.-London.
G‎. ‎E‎. ‎Sacks (1958). ‎Multiple error correction by means of parity-checks. IRE Trans.. IT-4, 145-147
S‎. ‎H‎. ‎Reiger (1960). ‎Codes for the correction of clustered errors. Trans‎. ‎IRE. IT-6, 16-21
A‎. ‎G‎. ‎Schillinger (1964). A class of solid burst error correcting codes. ‎Polytechnic Institute of Brooklyn‎, ‎N‎. ‎Y.‎, ‎Research Rept‎. ‎PIBMRI‎.
B‎. ‎D‎. ‎Sharma and B‎. ‎K‎. ‎Dass (1977). ‎Adjacent error correcting binary perfect codes. J‎. ‎Cybernetics. 7, 9-13
S‎. ‎G‎. ‎S‎. ‎Shiva and C‎. ‎L‎. ‎Sheng (1969). ‎Multiple solid burst-error-correcting binary codes. IEEE Trans‎. ‎Information Theory. IT-15, 188-189
Statistics
Article View: 3,644
PDF Download: 2,882