Error Detection and Correction Using Hamming and Cyclic Codes in a Communication Channel

Irene Ndanu John; Peter Waweru Kamaku; Dishon Kahuthu Macharia; Nicholas Muthama Mutua

doi:doi:10.11648/j.pamj.20160506.17

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Error Detection and Correction Using Hamming and Cyclic Codes in a Communication Channel

Irene Ndanu John, Peter Waweru Kamaku, Dishon Kahuthu Macharia, Nicholas Muthama Mutua

Published in Pure and Applied Mathematics Journal (Volume 5, Issue 6)

Received: 1 December 2016 Accepted: 28 December 2016 Published: 20 January 2017

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Abstract

This paper provides an overview of two types of linear block codes: Hamming and cyclic codes. We have generated, encoded and decoded these codes as well as schemes and/or algorithms of error-detecting and error-correcting of these codes. We have managed to detect and correct errors in a communication channel using error detection and correction schemes of hamming and cyclic codes.

Published in	Pure and Applied Mathematics Journal (Volume 5, Issue 6)
DOI	10.11648/j.pamj.20160506.17
Page(s)	220-231
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Linear Blocks, Hamming, Cyclic, Error-Detecting, Error-Correcting

References

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[3]	Doran R. Encyclopedia of Mathematics and its Applications. 2^nd ed. Cambridge University Press; 2002. 205.
[4]	Hall J. Notes on Coding Theory. United State America: Michigan State University. 2003. 10P.
[5]	Hamming R. Error Detecting and Error Correcting Codes. Bell Syst. Tech. J., 29. 1950; 147-160.
[6]	Han Y. Introduction to Binary Linear Block Codes. National Taipei University. Taiwan. 97P.
[7]	Kolman B. Introductory Linear Algebra: with Applications. 3^rd ed. United States of America: Prentice Hall; 1997. 608P.
[8]	Kabatiansky G. Error Correcting Coding and Security for Data Networks. John Wiley & Sons, Ltd; 2005. 278p.
[9]	Lemmermeyer F. Error Correcting Codes. 2005. 100P.
[10]	Nyaga, L. and Cecilia, M. (2008). Increasing error detection and correction efficiency in the ISBN. Discovery and Innovation, 20: 3–4.
[11]	Todd, K. M. (2005). Error Correction Coding: Mathematical Methods and Algorithms. John Wiley & Sons Inc.
[12]	Asma & Ramanjaneyulu [2015]: Implementation of Convolution Encoder and Adaptive Viterbi Decoder for Error Correction, International Journal of Emerging Engineering Research and Technology.
[13]	Egwali Annie O. and Akwukwuma V. V. N. (2013): Performance Evaluation of AN-VE: An Error Detection and Correction Code, African Journal of Computing & ICT.
[14]	Vikas Gupta, Chanderkant Verma (2012): Error Detection and Correction: Viterbi Mechanism, International Journal of Computer Science and Communication Engineering.
[15]	Neha Chauhan, Pooja Yadav, Preeti Kumari (2014): Error Detecting and Error Correcting Codes, International Journal of Innovative Research in Technology.

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APA Style

Irene Ndanu John, Peter Waweru Kamaku, Dishon Kahuthu Macharia, Nicholas Muthama Mutua. (2017). Error Detection and Correction Using Hamming and Cyclic Codes in a Communication Channel. Pure and Applied Mathematics Journal, 5(6), 220-231. https://doi.org/10.11648/j.pamj.20160506.17

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ACS Style

Irene Ndanu John; Peter Waweru Kamaku; Dishon Kahuthu Macharia; Nicholas Muthama Mutua. Error Detection and Correction Using Hamming and Cyclic Codes in a Communication Channel. Pure Appl. Math. J. 2017, 5(6), 220-231. doi: 10.11648/j.pamj.20160506.17

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AMA Style

Irene Ndanu John, Peter Waweru Kamaku, Dishon Kahuthu Macharia, Nicholas Muthama Mutua. Error Detection and Correction Using Hamming and Cyclic Codes in a Communication Channel. Pure Appl Math J. 2017;5(6):220-231. doi: 10.11648/j.pamj.20160506.17

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@article{10.11648/j.pamj.20160506.17,
  author = {Irene Ndanu John and Peter Waweru Kamaku and Dishon Kahuthu Macharia and Nicholas Muthama Mutua},
  title = {Error Detection and Correction Using Hamming and Cyclic Codes in a Communication Channel},
  journal = {Pure and Applied Mathematics Journal},
  volume = {5},
  number = {6},
  pages = {220-231},
  doi = {10.11648/j.pamj.20160506.17},
  url = {https://doi.org/10.11648/j.pamj.20160506.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20160506.17},
  abstract = {This paper provides an overview of two types of linear block codes: Hamming and cyclic codes. We have generated, encoded and decoded these codes as well as schemes and/or algorithms of error-detecting and error-correcting of these codes. We have managed to detect and correct errors in a communication channel using error detection and correction schemes of hamming and cyclic codes.},
 year = {2017}
}

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TY  - JOUR
T1  - Error Detection and Correction Using Hamming and Cyclic Codes in a Communication Channel
AU  - Irene Ndanu John
AU  - Peter Waweru Kamaku
AU  - Dishon Kahuthu Macharia
AU  - Nicholas Muthama Mutua
Y1  - 2017/01/20
PY  - 2017
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VL  - 5
IS  - 6
ER  -

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Author Information

Irene Ndanu John

Mathematics and Informatics Department, Taita Taveta University, Voi, Kenya
Peter Waweru Kamaku

Pure and Applied Mathematics Department, Jomo Kenyatta University of Agriculture and Technology, JKUAT, Nairobi, Kenya
Dishon Kahuthu Macharia

Mathematics and Informatics Department, Taita Taveta University, Voi, Kenya
Nicholas Muthama Mutua

Mathematics and Informatics Department, Taita Taveta University, Voi, Kenya

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APA Style

Irene Ndanu John, Peter Waweru Kamaku, Dishon Kahuthu Macharia, Nicholas Muthama Mutua. (2017). Error Detection and Correction Using Hamming and Cyclic Codes in a Communication Channel. Pure and Applied Mathematics Journal, 5(6), 220-231. https://doi.org/10.11648/j.pamj.20160506.17

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ACS Style

Irene Ndanu John; Peter Waweru Kamaku; Dishon Kahuthu Macharia; Nicholas Muthama Mutua. Error Detection and Correction Using Hamming and Cyclic Codes in a Communication Channel. Pure Appl. Math. J. 2017, 5(6), 220-231. doi: 10.11648/j.pamj.20160506.17

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AMA Style

Irene Ndanu John, Peter Waweru Kamaku, Dishon Kahuthu Macharia, Nicholas Muthama Mutua. Error Detection and Correction Using Hamming and Cyclic Codes in a Communication Channel. Pure Appl Math J. 2017;5(6):220-231. doi: 10.11648/j.pamj.20160506.17

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@article{10.11648/j.pamj.20160506.17,
  author = {Irene Ndanu John and Peter Waweru Kamaku and Dishon Kahuthu Macharia and Nicholas Muthama Mutua},
  title = {Error Detection and Correction Using Hamming and Cyclic Codes in a Communication Channel},
  journal = {Pure and Applied Mathematics Journal},
  volume = {5},
  number = {6},
  pages = {220-231},
  doi = {10.11648/j.pamj.20160506.17},
  url = {https://doi.org/10.11648/j.pamj.20160506.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20160506.17},
  abstract = {This paper provides an overview of two types of linear block codes: Hamming and cyclic codes. We have generated, encoded and decoded these codes as well as schemes and/or algorithms of error-detecting and error-correcting of these codes. We have managed to detect and correct errors in a communication channel using error detection and correction schemes of hamming and cyclic codes.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Error Detection and Correction Using Hamming and Cyclic Codes in a Communication Channel
AU  - Irene Ndanu John
AU  - Peter Waweru Kamaku
AU  - Dishon Kahuthu Macharia
AU  - Nicholas Muthama Mutua
Y1  - 2017/01/20
PY  - 2017
N1  - https://doi.org/10.11648/j.pamj.20160506.17
DO  - 10.11648/j.pamj.20160506.17
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 220
EP  - 231
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20160506.17
AB  - This paper provides an overview of two types of linear block codes: Hamming and cyclic codes. We have generated, encoded and decoded these codes as well as schemes and/or algorithms of error-detecting and error-correcting of these codes. We have managed to detect and correct errors in a communication channel using error detection and correction schemes of hamming and cyclic codes.
VL  - 5
IS  - 6
ER  -

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