Codes detecting, locating and correcting random errors occurring in multiple sub-blocks.
Keywords:Syndromes, Parity check digits, Bounds, Error locating codes
AbstractIn this paper, we study bounds on the number of check digits of linear codes that can detect multiple sub-blocks each affected by e or less random errors and can locate such corrupted multiple sub-blocks. Further, we obtain an upper bound on the number of check digits of linear codes which can correct such errors occurring in multiple sub-blocks. We also give examples of such codes.
P. K. Das, Codes Detecting and Locating Solid Burst Errors, Romanian Journal of Mathematics and Computer Science, Vol. 2 (2), pp. 1-10, (2012).
P. K. Das and L. K. Vashisht, Error Locating Codes By Using Blockwise-Tensor Product of Blockwise Detecting/Correcting Codes, Khayyam Journal of Mathematics, Vol. 2 (1), pp. 6-17, (2016).
P. K. Das, Location of Multiple Sub-Blocks with Burst Errors, Electronic Notes in Discrete Mathematics, Vol. 63, pp. 117-123, (2017).
B. K. Dass, Burst error locating linear codes, J. Inf. and Optimization Sciences, Vol. 3(1), pp. 77-80, (1982).
B. K. Dass and S. Madan, Repeated Burst Error Locating Linear Codes, Discrete Mathematics, Algorithms and Applications, Vol. 2 (2), pp. 181-188, (2010).
B. K. Dass and S. Madan, Blockwise Repeated Burst Error Correcting Linear Codes, Ratio Mathematica -Journal of Applied Mathematics, Vol. 20, pp. 97-126 (2010).
B. K. Dass and S. K. Muttoo, Comments on Error-locating Codes -A New Concept in Error Control, IEEE Transactions on Information Theory, Vol. 27 (1), 136, (1981).
B. K. Dass and V. Tyagi, Bounds on blockwise burst error correcting linear codes, Information Sciences, vol. 20 (3), pp. 167-164, (1980).
E. Fujiwara and M. Kitakami, A Class of Error-Locating Codes for Byte-Organized Memory Systems, IEEE Transactions on Information Theory, vol. 40 (6), pp. 1857-1865, (Nov. 1994).
W. H. Fong, Coding Bounds for Multiple Phased-Burst Correction and Single Burst Correction Codes, http://arxiv.org/pdf/1104.1408.pdf, (2011).
M. Kitakami and S. Jiang, Code Design and Decoding Methods for Burst Error Locating Codes, Proceedings of the 11th Pacific Rim International Symposium on Dependable Computing, (2005), (doi:10.1109/PRDC.2005.24).
M. Kitakami, S. Jiang and E. Fujiwara, Metrics of error locating codes, IEICE Trans. Fundamentals of Electronics, Communications and Computer, vol. E80-A(11), pp. 2117-2122 (1997).
W. W. Peterson and E. J. Weldon(Jr.), Error-Correcting Codes, 2nd edition, The MIT Press, Mass, (1972).
G. E. Sacks, Multiple error correction by means of parity-checks, IRE Trans. Inform. Theory, IT-4, pp. 145-147 (1958).
J. K. Wolf, On an extended class of error-locating codes, Information and Control, vol. 8, pp. 163-169 (1965).
J. K. Wolf, On Codes Derivable from the Tensor Product of Check Matrices, IEEE Trans. on Inform. Theory, vol. 11 (2), pp. 281-284 (1965)
J. K. Wolf and B. Elspas, Error-locating codes—a new concept in error control. IEEE Trans. Inform. Theory IT-9, pp. 20-28, (1963).