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<datestamp>2018-01-11</datestamp>
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<title lang=en>Group structure on projective spaces and cyclic codes over finite fields</title>
<creator>Lachaud, Gilles</creator>
<creator>Lucien, Isabelle</creator>
<creator>Mercier, Dany-Jack</creator>
<creator>Rolland, Robert</creator>
<contributor>Institut de mathématiques de Luminy (IML) ; Centre National de la Recherche Scientifique (CNRS) - Université de la Méditerranée - Aix-Marseille 2</contributor>
<contributor>Equipe Applications de l'Algèbre et de l'Arithmétique ; Département de Mathématiques et Informatique (D.M.I.) ; Université des Antilles et de la Guyane (UAG) - Université des Antilles (Pôle Guadeloupe) ; Université des Antilles (UA) - Université des Antilles (UA) - Université des Antilles et de la Guyane (UAG) - Université des Antilles (Pôle Guadeloupe) ; Université des Antilles (UA) - Université des Antilles (UA)</contributor>
<contributor>Institut universitaire de formation des maîtres - Guadeloupe (IUFM Guadeloupe) ; Université des Antilles et de la Guyane (UAG)</contributor>
<description>International audience</description>
<source>ISSN: 1071-5797</source>
<source>EISSN: 1090-2465</source>
<source>Finite Fields and Their Applications</source>
<publisher>Elsevier</publisher>
<identifier>hal-00770256</identifier>
<identifier>https://hal.univ-antilles.fr/hal-00770256</identifier>
<source>https://hal.univ-antilles.fr/hal-00770256</source>
<source>Finite Fields and Their Applications, Elsevier, 2000, 6 (2), pp.119-129. 〈10.1006/ffta.1999.0268〉</source>
<identifier>DOI : 10.1006/ffta.1999.0268</identifier>
<relation>info:eu-repo/semantics/altIdentifier/doi/10.1006/ffta.1999.0268</relation>
<language>en</language>
<subject lang=en>reed-Muller</subject>
<subject lang=en>cyclic codes</subject>
<subject lang=en>error corroe corecting codes</subject>
<subject>[MATH.MATH-AC] Mathematics [math]/Commutative Algebra [math.AC]</subject>
<type>info:eu-repo/semantics/article</type>
<type>Journal articles</type>
<description lang=en>We study the geometrical properties of the subgroups of the multiplicative group of a finite extension of a finite field endowed with its vector space structure, and we show that in some cases the associated projective space has a natural groupe 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 of the Reed-Muller kind.</description>
<date>2000-04-01</date>
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