Bounds on linear codes capable of detecting, locating and correcting of repeated burst errors prevailing in multiple sub-blocks
DOI:
https://doi.org/10.22199/issn.0717-6279-2020-06-0094Keywords:
Syndromes, Parity check matrix, Bound, Burst, Repeated burstAbstract
Linear codes are presented that can detect, locate and correct all repeated burst errors of length b or less which occur in multiple sub-blocks. We obtain lower and upper bounds on the number of check digits for the existence of these codes. Three examples, one for each type of code, are provided.
References
[1] L. Berardi, B. K. Dass, and R. Verma, “On 2-repeated burst error detecting linear codes”, Journal of statistical theory and practice, vol. 3, no. 2, pp. 381-391, Jun.2009, doi: 10.1080/15598608.2009.10411931
[2] P. K. Das, “Location of multiple sub-blocks with burst errors”, Electronic notes in discrete mathematics, vol. 63, pp. 117-123, Dec. 2017, doi: 10.1016/j.endm.2017.11.006
[3] P. K. Das, “Codes detecting, locating and correcting random errors occurring in multiple sub-blocks”, Proyecciones (Antofagasta. En línea), vol. 38, no. 1, pp. 129-144, Mar. 2019, doi: 10.4067/S0716-09172019000100129
[4] P. K. Das and L. K. Vashisht, “Error locating codes by using blockwisetensor product of blockwise detecting/correcting codes”, Khayyam journal of mathematics, vol. 2, no. 1, pp. 6-17, 2016, doi: 10.22034/KJM.2016.14572
[5] B. K. Dass and R. Verma, “Repeated burst error correcting linear codes”, Asian-european journal of mathematics, vol. 1, no. 3, pp. 303-335, 2008, doi: 10.1142/S1793557108000278
[6] B. K. Dass and R. Verma, “Repeated burst error detecting linear codes”, Ratio mathematica, vol. 19, pp. 25-30, 2009. [On line]. Available: https://bit.ly/3eosbVj
[7] B. K. Dass and S. Madan, “Blockwise repeated burst error correcting linear codes”, Ratio mathematica, vol. 20, pp. 97-126, 2010. [On line]. Available: https://bit.ly/3eqLqxf
[8] B. K. Dass and S. Madan, “Repeated burst error locating linear codes”, Discrete mathematics, algorithms and applications, vol. 2, no. 2, pp. 181-188, 2010, doi: 10.1142/S1793830910000553
[9] P. Fire, "A class of multiple-error-correction binary codes for nonindependent errors", Thesis Engineer, Stanford University, Dept. of Electrical Engineering., 1959.
[10] W. W. Peterson and E. J. Weldon, Error correcting codes, 2nd ed. Cambridge, MA: MIT Press, 1972.
[11] G. E. Sacks, “Multiple error correction by means of parity-checks”, IRE transactions on information theory, vol. 4, no. 4, pp. 145-147, Dec. 1958, doi: 10.1109/IRETIT.1958.6741947
[12] J. K. Wolf, “On an extended class of error-locating codes”, Information and control, vol. 8, no. 2, pp. 163-169, Apr.1965, doi: 10.1016/S0019-9958(65)90066-5
[13] J. K. Wolf and B. Elspas, "Error-locating codes--A new concept in error control", IEEE transactions on information theory, vol. 9, no. 2, pp. 113-117, Apr.1963, doi: 10.1109/TIT.1963.1057813
[14] J. M. Wozencraft, “Sequential decoding for reliable communication”, IRE National Convention Record, vol. 5, no. 2, pp. 11-25, 1957.
[2] P. K. Das, “Location of multiple sub-blocks with burst errors”, Electronic notes in discrete mathematics, vol. 63, pp. 117-123, Dec. 2017, doi: 10.1016/j.endm.2017.11.006
[3] P. K. Das, “Codes detecting, locating and correcting random errors occurring in multiple sub-blocks”, Proyecciones (Antofagasta. En línea), vol. 38, no. 1, pp. 129-144, Mar. 2019, doi: 10.4067/S0716-09172019000100129
[4] P. K. Das and L. K. Vashisht, “Error locating codes by using blockwisetensor product of blockwise detecting/correcting codes”, Khayyam journal of mathematics, vol. 2, no. 1, pp. 6-17, 2016, doi: 10.22034/KJM.2016.14572
[5] B. K. Dass and R. Verma, “Repeated burst error correcting linear codes”, Asian-european journal of mathematics, vol. 1, no. 3, pp. 303-335, 2008, doi: 10.1142/S1793557108000278
[6] B. K. Dass and R. Verma, “Repeated burst error detecting linear codes”, Ratio mathematica, vol. 19, pp. 25-30, 2009. [On line]. Available: https://bit.ly/3eosbVj
[7] B. K. Dass and S. Madan, “Blockwise repeated burst error correcting linear codes”, Ratio mathematica, vol. 20, pp. 97-126, 2010. [On line]. Available: https://bit.ly/3eqLqxf
[8] B. K. Dass and S. Madan, “Repeated burst error locating linear codes”, Discrete mathematics, algorithms and applications, vol. 2, no. 2, pp. 181-188, 2010, doi: 10.1142/S1793830910000553
[9] P. Fire, "A class of multiple-error-correction binary codes for nonindependent errors", Thesis Engineer, Stanford University, Dept. of Electrical Engineering., 1959.
[10] W. W. Peterson and E. J. Weldon, Error correcting codes, 2nd ed. Cambridge, MA: MIT Press, 1972.
[11] G. E. Sacks, “Multiple error correction by means of parity-checks”, IRE transactions on information theory, vol. 4, no. 4, pp. 145-147, Dec. 1958, doi: 10.1109/IRETIT.1958.6741947
[12] J. K. Wolf, “On an extended class of error-locating codes”, Information and control, vol. 8, no. 2, pp. 163-169, Apr.1965, doi: 10.1016/S0019-9958(65)90066-5
[13] J. K. Wolf and B. Elspas, "Error-locating codes--A new concept in error control", IEEE transactions on information theory, vol. 9, no. 2, pp. 113-117, Apr.1963, doi: 10.1109/TIT.1963.1057813
[14] J. M. Wozencraft, “Sequential decoding for reliable communication”, IRE National Convention Record, vol. 5, no. 2, pp. 11-25, 1957.
Published
2020-11-12 — Updated on 2020-11-19
How to Cite
[1]
P. K. Das and S. Kumar, “Bounds on linear codes capable of detecting, locating and correcting of repeated burst errors prevailing in multiple sub-blocks”, Proyecciones (Antofagasta, On line), vol. 39, no. 6, pp. 1577-1596, Nov. 2020.
Issue
Section
Artículos
Copyright (c) 2020 Pankaj Kumar Das, Subodh Kumar
This work is licensed under a Creative Commons Attribution 4.0 International License.
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
