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On Cyclic Codes of a Given Length N

Published on May 2012 by Manjit Singh
journal_cover_thumbnail

National Workshop-Cum-Conference on Recent Trends in Mathematics and Computing 2011
Foundation of Computer Science USA
RTMC - Number 10
May 2012
Authors: Manjit Singh
939bade6-6ca5-43c8-8ce9-aafa202f2db8

Manjit Singh . On Cyclic Codes of a Given Length N. National Workshop-Cum-Conference on Recent Trends in Mathematics and Computing 2011. RTMC, 10 (May 2012), 21-25.

@article{
author = { Manjit Singh },
title = { On Cyclic Codes of a Given Length N },
journal = { National Workshop-Cum-Conference on Recent Trends in Mathematics and Computing 2011 },
issue_date = { May 2012 },
volume = { RTMC },
number = { 10 },
month = { May },
year = { 2012 },
issn = 0975-8887,
pages = { 21-25 },
numpages = 5,
url = { /proceedings/rtmc/number10/6694-1082/ },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Proceeding Article
%1 National Workshop-Cum-Conference on Recent Trends in Mathematics and Computing 2011
%A Manjit Singh
%T On Cyclic Codes of a Given Length N
%J National Workshop-Cum-Conference on Recent Trends in Mathematics and Computing 2011
%@ 0975-8887
%V RTMC
%N 10
%P 21-25
%D 2012
%I International Journal of Computer Applications
Abstract

The theory of Error–correcting codes is eminently indispensable in our life. In this direction, one of the most important developments was the theory of cyclic codes, which is traditionally embedded in the language of ring theory. In this paper our interest to motivate the ring theoretic formulation of coding theory and draw attention to the paths used to determine the cyclic codes generated by the idempotent generators in the ring ? ? 1 N N q R ? F X X ? of a given length N over the finite field q F with explicit settings.

References
  1. S. K. Arora and M. Pruthi, Minimal cyclic codes of length , Finite Field and 2 n p
  2. Appl. , 5(1999), 177-187.
  3. J. H. van Lint. Introduction to Coding Theory, Springer-Verlag, Berlin- Heidelberg, 3rd revised and expended ed. edition, 1982-1999.
  4. Vera Pless, Introduction to the Theory of Error-Correcting Codes, A Wiley – Interscience Publication, New York, Toronto, 1981.
  5. L. R. Vermani, Elements of algebraic coding theory,Chapman and Hall Mathematics,1964. .
  6. S. K. Arora, Sudhir Batra ,S. D. Cohen and Manju Pruthi,The Primitive Idempotents of a Cyclic Group Algebra , Southeast Asian Bulletin of Mathematics (2002) 26:549-557.
  7. S. Batra , S. K. Arora. :Minimal Quadratic Residues Cyclic Codes of length ,The Korean Journal of Computational and Applied Mathematics 8(3), 531-547(2001). n p
  8. E. Prange,Cyclic error-correcting codes with two symbols,AFCRC-TN-57-103 September (1957).
Index Terms

Computer Science
Information Sciences

Keywords

Cyclic Codes Ternary Cyclic Codes