Maximal hypersurfaces of degree d in Pn(Fq) and minimum weight spectrum of the generalized PRM(q, d, n)-code

We give an intrinsic projective configuration of the maximal hypersurfaces of degree d in P n ( F q ) . It is a particular arrangement of hyperplanes containing subarrangements of hyperplanes in general position. This characterization allows us to compute the number of minimum distance codewords of...

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Bibliographic Details
Published in:Journal of geometry 2024-04, Vol.115 (1)
Main Author: Sboui, Adnen
Format: Article
Language:English
Subjects:
Geometry
Hyperplanes
Hyperspaces
Mathematics
Mathematics and Statistics
Minimum weight
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Summary:We give an intrinsic projective configuration of the maximal hypersurfaces of degree d in P n ( F q ) . It is a particular arrangement of hyperplanes containing subarrangements of hyperplanes in general position. This characterization allows us to compute the number of minimum distance codewords of the projective Reed-Muller code PRM ( q ,  d ,  n ).
ISSN:0047-2468
1420-8997
DOI:10.1007/s00022-024-00713-w