On the Number of Points of Some Hypersurfaces in F n q
Identifieur interne : 003174 ( Istex/Corpus ); précédent : 003173; suivant : 003175On the Number of Points of Some Hypersurfaces in F n q
Auteurs : Jean Pierre Cherdieu ; Robert RollandSource :
- 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
Links to Exploration step
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