On the Number of Points of Some Hypersurfaces in F n q
Identifieur interne : 001865 ( Istex/Checkpoint ); précédent : 001864; suivant : 001866On the Number of Points of Some Hypersurfaces in F n q
Auteurs : Jean Pierre Cherdieu [France] ; Robert Rolland [France]Source :
- Finite Fields and Their Applications [ 1071-5797 ] ; 1996.
English descriptors
- KwdEn :
- Academic press, Common subspace, Generalized code, Generalized codes, Hyperplane, Hyperplane arrangement, Hyperplane arrangements, Hyperplane intersects, Hyperplanes, Hypersurfaces, Irreducible, Irreducible factor, Irreducible polynomial, Linear functions, Maximum number, Mobius function, Mobius functions, Other hyperplanes, Parallel hyperplanes, Polynomial function, Polynomial functions, Rolland proof, Strict inequality, Total degree, Total number.
- Teeft :
- Academic press, Common subspace, Generalized code, Generalized codes, Hyperplane, Hyperplane arrangement, Hyperplane arrangements, Hyperplane intersects, Hyperplanes, Hypersurfaces, Irreducible, Irreducible factor, Irreducible polynomial, Linear functions, Maximum number, Mobius function, Mobius functions, Other hyperplanes, Parallel hyperplanes, Polynomial function, Polynomial functions, Rolland proof, Strict inequality, Total degree, Total number.
Abstract
Abstract: For generalized Reed–Muller codes, whenqis large enough, we give the second codeword weight, that is, the weight which is just above the minimal distance, and we also list all the codewords which reach this weight. To do this we have to study the number of points of some hypersurfaces and some arrangements of hyperplanes. We also present some properties of the Möbius function of these arrangements.
Url:
DOI: 10.1006/ffta.1996.0014
Affiliations:
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ISTEX:F2EB826A7E2F2BA590B9CB8C07C883F08D0D433ELe document en format XML
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Laboratoire de Mathématiques Discrètes, Luminy Case 930, F13288, Marseille Cedex 9, France</wicri:regionArea><wicri:noRegion>France</wicri:noRegion><wicri:noRegion>France</wicri:noRegion></affiliation></author></analytic><monogr></monogr><series><title level="j">Finite Fields and Their Applications</title><title level="j" type="abbrev">YFFTA</title><idno type="ISSN">1071-5797</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="1996">1996</date><biblScope unit="volume">2</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="214">214</biblScope><biblScope unit="page" to="224">224</biblScope></imprint><idno type="ISSN">1071-5797</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">1071-5797</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Academic press</term><term>Common subspace</term><term>Generalized code</term><term>Generalized codes</term><term>Hyperplane</term><term>Hyperplane arrangement</term><term>Hyperplane arrangements</term><term>Hyperplane intersects</term><term>Hyperplanes</term><term>Hypersurfaces</term><term>Irreducible</term><term>Irreducible factor</term><term>Irreducible polynomial</term><term>Linear functions</term><term>Maximum number</term><term>Mobius function</term><term>Mobius functions</term><term>Other hyperplanes</term><term>Parallel hyperplanes</term><term>Polynomial function</term><term>Polynomial functions</term><term>Rolland proof</term><term>Strict inequality</term><term>Total degree</term><term>Total number</term></keywords><keywords scheme="Teeft" xml:lang="en"><term>Academic press</term><term>Common subspace</term><term>Generalized code</term><term>Generalized codes</term><term>Hyperplane</term><term>Hyperplane arrangement</term><term>Hyperplane arrangements</term><term>Hyperplane intersects</term><term>Hyperplanes</term><term>Hypersurfaces</term><term>Irreducible</term><term>Irreducible factor</term><term>Irreducible polynomial</term><term>Linear functions</term><term>Maximum number</term><term>Mobius function</term><term>Mobius functions</term><term>Other hyperplanes</term><term>Parallel hyperplanes</term><term>Polynomial function</term><term>Polynomial functions</term><term>Rolland proof</term><term>Strict inequality</term><term>Total degree</term><term>Total number</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: For generalized Reed–Muller codes, whenqis large enough, we give the second codeword weight, that is, the weight which is just above the minimal distance, and we also list all the codewords which reach this weight. To do this we have to study the number of points of some hypersurfaces and some arrangements of hyperplanes. We also present some properties of the Möbius function of these arrangements.</div></front></TEI><affiliations><list><country><li>France</li></country></list><tree><country name="France"><noRegion><name sortKey="Cherdieu, Jean Pierre" sort="Cherdieu, Jean Pierre" uniqKey="Cherdieu J" first="Jean Pierre" last="Cherdieu">Jean Pierre Cherdieu</name></noRegion><name sortKey="Rolland, Robert" sort="Rolland, Robert" uniqKey="Rolland R" first="Robert" last="Rolland">Robert Rolland</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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