Transform domain characterization of cyclic codes over Zm

Cyclic codes with symbols from a residue class integer ring Zm are characterized in terms of the discrete Fourier transform (DFT) of codewords defined over an appropriate extension ring of Zm. It is shown that a cyclic code of length n over Zm, n relatively prime to m, consists of n-tuples over Zm h...

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Main Authors:	Rajan, Sundar B., Siddiqi, Mohammad Umar
Format:	Article
Language:	English
Published:	Springer Verlag 1994
Subjects:	TK5101 Telecommunication. Including telegraphy, radio, radar, television
Online Access:	http://irep.iium.edu.my/14203/ http://irep.iium.edu.my/14203/ http://irep.iium.edu.my/14203/ http://irep.iium.edu.my/14203/1/72e7e51a6f4206c0c7.pdf

id	iium-14203
recordtype	eprints
spelling	iium-142032013-07-22T04:00:59Z http://irep.iium.edu.my/14203/ Transform domain characterization of cyclic codes over Zm Rajan, Sundar B. Siddiqi, Mohammad Umar TK5101 Telecommunication. Including telegraphy, radio, radar, television Cyclic codes with symbols from a residue class integer ring Zm are characterized in terms of the discrete Fourier transform (DFT) of codewords defined over an appropriate extension ring of Zm. It is shown that a cyclic code of length n over Zm, n relatively prime to m, consists of n-tuples over Zm having a specified set of DFT coefficients from the elements of an ideal of a subring of the extension ring. When m is equal to a product of distinct primes every cyclic code over Zm has an idempotent generator and it is shown that the idempotent generators can be easily identified in the transform domain. The dual code pairs over Zm are characterized in the transform domain for cyclic codes. Necessary and sufficient conditions for the existence of self-dual codes over Zm are obtained and nonexistence of self-dual codes for certain values of m is proved. Springer Verlag 1994 Article PeerReviewed application/pdf en http://irep.iium.edu.my/14203/1/72e7e51a6f4206c0c7.pdf Rajan, Sundar B. and Siddiqi, Mohammad Umar (1994) Transform domain characterization of cyclic codes over Zm. Applicable Algebra in Engineering, Communications and Computing, 5 (5). pp. 261-275. ISSN 0938-1279 http://link.springer.com/article/10.1007/BF01225641 10.1007/BF01225641
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	TK5101 Telecommunication. Including telegraphy, radio, radar, television
spellingShingle	TK5101 Telecommunication. Including telegraphy, radio, radar, television Rajan, Sundar B. Siddiqi, Mohammad Umar Transform domain characterization of cyclic codes over Zm
description	Cyclic codes with symbols from a residue class integer ring Zm are characterized in terms of the discrete Fourier transform (DFT) of codewords defined over an appropriate extension ring of Zm. It is shown that a cyclic code of length n over Zm, n relatively prime to m, consists of n-tuples over Zm having a specified set of DFT coefficients from the elements of an ideal of a subring of the extension ring. When m is equal to a product of distinct primes every cyclic code over Zm has an idempotent generator and it is shown that the idempotent generators can be easily identified in the transform domain. The dual code pairs over Zm are characterized in the transform domain for cyclic codes. Necessary and sufficient conditions for the existence of self-dual codes over Zm are obtained and nonexistence of self-dual codes for certain values of m is proved.
format	Article
author	Rajan, Sundar B. Siddiqi, Mohammad Umar
author_facet	Rajan, Sundar B. Siddiqi, Mohammad Umar
author_sort	Rajan, Sundar B.
title	Transform domain characterization of cyclic codes over Zm
title_short	Transform domain characterization of cyclic codes over Zm
title_full	Transform domain characterization of cyclic codes over Zm
title_fullStr	Transform domain characterization of cyclic codes over Zm
title_full_unstemmed	Transform domain characterization of cyclic codes over Zm
title_sort	transform domain characterization of cyclic codes over zm
publisher	Springer Verlag
publishDate	1994
url	http://irep.iium.edu.my/14203/ http://irep.iium.edu.my/14203/ http://irep.iium.edu.my/14203/ http://irep.iium.edu.my/14203/1/72e7e51a6f4206c0c7.pdf
first_indexed	2023-09-18T20:23:23Z
last_indexed	2023-09-18T20:23:23Z
_version_	1777408256071696384

Transform domain characterization of cyclic codes over Zm

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