Group Structure on Projective Spaces and Cyclic Codes over Finite Fields
نویسندگان
چکیده
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. ( 2000 Academic Press Key =ords: Error correcting codes, cyclic codes, Reed}Muller codes. AMS 1991 Mathematics Subject Classixcation: 94B05.
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تاریخ انتشار 1999