A note on the weight distribution of some cyclic codes

Let Fq be the finite field with q elements and Cn be the cyclic group of order n, where n is a positive integer relatively prime to q . Let H,K be subgroups of Cn such that H is a proper subgroup of K. In this note, the weight distributions of the cyclic codes of length n over Fq with generatin...

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Main Authors: Lin, Liren, Chen, Bocong, Liu, Hongwei
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2015
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Online Access:https://hdl.handle.net/10356/107455
http://hdl.handle.net/10220/25502
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1074552023-02-28T19:47:50Z A note on the weight distribution of some cyclic codes Lin, Liren Chen, Bocong Liu, Hongwei School of Physical and Mathematical Sciences DRNTU::Science::Physics::Atomic physics::Field theories Let Fq be the finite field with q elements and Cn be the cyclic group of order n, where n is a positive integer relatively prime to q . Let H,K be subgroups of Cn such that H is a proper subgroup of K. In this note, the weight distributions of the cyclic codes of length n over Fq with generating idempotents View the MathML source and View the MathML source are explicitly determined, where View the MathML source and View the MathML source. Our result naturally gives a new characterization of a theorem by Sharma and Bakshi [18] that determines the weight distribution of all irreducible cyclic codes of length pm over Fq, where p is an odd prime and q is a primitive root modulo pm. Finally, two examples are presented to illustrate our results. Accepted version 2015-05-11T06:37:09Z 2019-12-06T22:31:32Z 2015-05-11T06:37:09Z 2019-12-06T22:31:32Z 2015 2015 Journal Article Lin, L., Chen, B., & Liu, H. (2015). A note on the weight distribution of some cyclic codes. Finite fields and their applications, 35, 78–85. 1071-5797 https://hdl.handle.net/10356/107455 http://hdl.handle.net/10220/25502 10.1016/j.ffa.2015.03.003 185847 en Finite fields and their applications © 2015 Elsevier. This is the author created version of a work that has been peer reviewed and accepted for publication by Finite Fields and Their Applications, Elsevier. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1016/j.ffa.2015.03.003]. 6 p. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic DRNTU::Science::Physics::Atomic physics::Field theories
spellingShingle DRNTU::Science::Physics::Atomic physics::Field theories
Lin, Liren
Chen, Bocong
Liu, Hongwei
A note on the weight distribution of some cyclic codes
description Let Fq be the finite field with q elements and Cn be the cyclic group of order n, where n is a positive integer relatively prime to q . Let H,K be subgroups of Cn such that H is a proper subgroup of K. In this note, the weight distributions of the cyclic codes of length n over Fq with generating idempotents View the MathML source and View the MathML source are explicitly determined, where View the MathML source and View the MathML source. Our result naturally gives a new characterization of a theorem by Sharma and Bakshi [18] that determines the weight distribution of all irreducible cyclic codes of length pm over Fq, where p is an odd prime and q is a primitive root modulo pm. Finally, two examples are presented to illustrate our results.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Lin, Liren
Chen, Bocong
Liu, Hongwei
format Article
author Lin, Liren
Chen, Bocong
Liu, Hongwei
author_sort Lin, Liren
title A note on the weight distribution of some cyclic codes
title_short A note on the weight distribution of some cyclic codes
title_full A note on the weight distribution of some cyclic codes
title_fullStr A note on the weight distribution of some cyclic codes
title_full_unstemmed A note on the weight distribution of some cyclic codes
title_sort note on the weight distribution of some cyclic codes
publishDate 2015
url https://hdl.handle.net/10356/107455
http://hdl.handle.net/10220/25502
_version_ 1759857347297017856