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 |
Linear Blocks, Hamming, Cyclic, Error-Detecting, Error-Correcting
[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. |
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
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
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
@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} }
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 -