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Group Structure on Projective Spaces and Cyclic Codes over Finite Fields

✍ Scribed by Gilles Lachaud; Isabelle Lucien; Dany-Jack Mercier; Robert Rolland

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 124 KB
Volume: 6
Category: Article
ISSN: 1071-5797
DOI: 10.1006/ffta.1999.0268

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✦ Synopsis

We study the geometrical properties of the subgroups of the mutliplicative group of a "nite extension of a "nite "eld endowed with its vector space structure and we show that in some cases the associated projective space has a natural group structure. We construct some cyclic codes related to Reed}Muller codes by evaluating polynomials on these subgroups. The geometrical properties of these groups give a fairly simple description of these codes which are of the Reed}Muller kind.

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