Study of idempotents in cyclic group rings over F2

Kai Lin Ong; Miin Huey Ang

doi:10.1063/1.4952491

Study of idempotents in cyclic group rings over F₂

Kai Lin Ong, Miin Huey Ang^*

^*Corresponding author for this work

School of Mathematical & Computer Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

4 Citations (Scopus)

Abstract

The existence of an idempotent generator for group codes or group ring codes in F_qG plays a very important role in determining the minimal distance of the respective code. Some necessary and sufficient conditions for a group ring element to be an idempotent in F₂C_n are investigated in this paper. The main result in this paper is the affirmation of the existence of finitely many basis idempotents which gives a full identification of all idempotents in every binary cyclic group ring F₂C_n. All the basis idempotents in F₂C_n are able to be found by partitioning the largest idempotent's support.

Original language	English
Title of host publication	Innovations Through Mathematical and Statistical Research
Subtitle of host publication	Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics (ICMSS2016)
Publisher	AIP Publishing
ISBN (Electronic)	9780735413962
DOIs	https://doi.org/10.1063/1.4952491
Publication status	Published - 2 Jun 2016
Event	2nd International Conference on Mathematical Sciences and Statistics: Innovations Through Mathematical and Statistical Research - Kuala Lumpur, Malaysia Duration: 26 Jan 2016 → 28 Jan 2016

Publication series

Name	AIP Conference Proceedings
Volume	1739
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	2nd International Conference on Mathematical Sciences and Statistics
Abbreviated title	ICMSS 2016
Country/Territory	Malaysia
City	Kuala Lumpur
Period	26/01/16 → 28/01/16

ASJC Scopus subject areas

General Physics and Astronomy

Access to Document

10.1063/1.4952491

Cite this

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title = "Study of idempotents in cyclic group rings over F2",

abstract = "The existence of an idempotent generator for group codes or group ring codes in FqG plays a very important role in determining the minimal distance of the respective code. Some necessary and sufficient conditions for a group ring element to be an idempotent in F2Cn are investigated in this paper. The main result in this paper is the affirmation of the existence of finitely many basis idempotents which gives a full identification of all idempotents in every binary cyclic group ring F2Cn. All the basis idempotents in F2Cn are able to be found by partitioning the largest idempotent's support.",

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Ong, KL & Ang, MH 2016, Study of idempotents in cyclic group rings over F₂. in Innovations Through Mathematical and Statistical Research: Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics (ICMSS2016)., 020011, AIP Conference Proceedings, vol. 1739, AIP Publishing, 2nd International Conference on Mathematical Sciences and Statistics, Kuala Lumpur, Malaysia, 26/01/16. https://doi.org/10.1063/1.4952491

Study of idempotents in cyclic group rings over F₂. / Ong, Kai Lin; Ang, Miin Huey.
Innovations Through Mathematical and Statistical Research: Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics (ICMSS2016). AIP Publishing, 2016. 020011 (AIP Conference Proceedings; Vol. 1739).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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