Study of idempotents in cyclic group rings over F{sub 2}

Journal Article · Thu Jun 02 00:00:00 EDT 2016 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.4952491· OSTI ID:22609039

Ong, Kai Lin, E-mail: [e-mail]; Ang, Miin Huey, E-mail: [e-mail] ^[1]

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1. Pusat Pengajian Sains Matematik, Universiti Sains Malaysia, Minden 11800, Penang Malaysia (Malaysia)

The existence of an idempotent generator for group codes or group ring codes in F{sub q}G 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 F{sub 2}C{sub 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 F{sub 2}C{sub n}. All the basis idempotents in F{sub 2}C{sub n} are able to be found by partitioning the largest idempotent’s support.

• OSTI ID: 22609039
• Journal Information: AIP Conference Proceedings, Vol. 1739, Issue 1; Conference: ICMSS2016: 2. international conference on mathematical sciences and statistics, Kuala Lumpur (Malaysia), 26-28 Jan 2016; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
BASES
DISTANCE
MATHEMATICAL MODELS
MATHEMATICAL SPACE
PARTITION