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:
Links toward previous steps (curation, corpus...)
Links to Exploration step
ISTEX:F2EB826A7E2F2BA590B9CB8C07C883F08D0D433ELe document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">On the Number of Points of Some Hypersurfaces in F n q</title>
<author><name sortKey="Cherdieu, Jean Pierre" sort="Cherdieu, Jean Pierre" uniqKey="Cherdieu J" first="Jean Pierre" last="Cherdieu">Jean Pierre Cherdieu</name>
</author>
<author><name sortKey="Rolland, Robert" sort="Rolland, Robert" uniqKey="Rolland R" first="Robert" last="Rolland">Robert Rolland</name>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:F2EB826A7E2F2BA590B9CB8C07C883F08D0D433E</idno>
<date when="1996" year="1996">1996</date>
<idno type="doi">10.1006/ffta.1996.0014</idno>
<idno type="url">https://api.istex.fr/document/F2EB826A7E2F2BA590B9CB8C07C883F08D0D433E/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">003174</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">003174</idno>
<idno type="wicri:Area/Istex/Curation">003174</idno>
<idno type="wicri:Area/Istex/Checkpoint">001865</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">001865</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">On the Number of Points of Some Hypersurfaces in F n q</title>
<author><name sortKey="Cherdieu, Jean Pierre" sort="Cherdieu, Jean Pierre" uniqKey="Cherdieu J" first="Jean Pierre" last="Cherdieu">Jean Pierre Cherdieu</name>
<affiliation wicri:level="1"><country wicri:rule="url">France</country>
<wicri:regionArea>Département de Mathématiques Informatique, Université des Antilles et de la Guyane, Campus de Fouillole, F97159, Pointe-à-Pitre Cedex, France</wicri:regionArea>
<wicri:noRegion>France</wicri:noRegion>
<wicri:noRegion>France</wicri:noRegion>
</affiliation>
</author>
<author><name sortKey="Rolland, Robert" sort="Rolland, Robert" uniqKey="Rolland R" first="Robert" last="Rolland">Robert Rolland</name>
<affiliation wicri:level="1"><country wicri:rule="url">France</country>
<wicri:regionArea>C.N.R.S. 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)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Istex/Checkpoint
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 001865 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Istex/Checkpoint/biblio.hfd -nk 001865 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Mathematiques |area= BourbakiV1 |flux= Istex |étape= Checkpoint |type= RBID |clé= ISTEX:F2EB826A7E2F2BA590B9CB8C07C883F08D0D433E |texte= On the Number of Points of Some Hypersurfaces in F n q }}
![]() | This area was generated with Dilib version V0.6.33. | ![]() |