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Application of Karnaugh map for easy generation of error correcting codes

Tabandeh, M ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1016/j.scient.2011.08.030
  3. Publisher: 2012
  4. Abstract:
  5. With increasing use of data transmission between digital systems as well as subsystems, the need for more reliable communication is felt. In this research, a new approach to the linear error correcting codes is introduced. Among advantages of this technique are simpler code construction and also decoding algorithm, as well as easier understanding of the basic concept. Based on an earlier paper and also recent work done, we first discuss briefly the use of Karnaugh map and its advantages in constructing simple codes. We then prove a theorem on application of the map to multiple error correcting codes. Using these results, we propose a simple technique that leads to obtaining a code with more capabilities. We also discuss another advantage of using the Karnaugh map in error correcting codes. As an example, we discuss a special case of generating a double error correcting code and using Karnaugh map features to give it extended capabilities
  6. Keywords:
  7. Code-words ; Hamming type code ; K-code ; Karnaugh maps ; Linear codes ; S-map ; Data communication systems ; Hamming distance ; Error correction ; Algorithm ; Data transmission ; Error analysis ; Linearity ; Mathematical theory
  8. Source: Scientia Iranica ; Volume 19, Issue 3 , June , 2012 , Pages 690-695 ; 10263098 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S1026309811001805