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

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), 2017. Published by Science Publishing Group

Keywords

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

References
[1] Attarian Ad. Algebraic Coding Theory. 2006. 12P.
[2] Blahut R. Algebraic Codes for Data Transmission. United Kingdom: Cambridge University Press; 2003. 482p.
[3] Doran R. Encyclopedia of Mathematics and its Applications. 2nd 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. 3rd 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.
Cite This Article
  • 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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    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
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    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
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Author Information
  • Mathematics and Informatics Department, Taita Taveta University, Voi, Kenya

  • Pure and Applied Mathematics Department, Jomo Kenyatta University of Agriculture and Technology, JKUAT, Nairobi, Kenya

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

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

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