On the number of points of some hypersurfaces in \(\mathbb{F}^n_q\)

DOI10.1006/ffta.1996.0014zbMath0899.94025OpenAlexW1981111533MaRDI QIDQ1383500

Jean Pierre Cherdieu, Robert Rolland

Publication date: 26 April 1998

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/ffta.1996.0014

zbMATH Keywords

Möbius functionarrangements of hyperplanesgeneralized Reed-Muller codespoints of hypersurfacessecond codeword weight

Mathematics Subject Classification ID

Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Linear codes and caps in Galois spaces (51E22) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Cyclic codes (94B15)

Related Items (15)

Second highest number of points of hypersurfaces in \(\mathbb F_q^n\) ⋮ The second weight of generalized Reed-Muller codes in most cases ⋮ A note on diagonal and Hermitian hypersurfaces ⋮ Minimal and maximal arrangements of hyperplanes in \(\mathbb P^{n}(\mathbb {F}_{q})\) ⋮ Second weight codewords of generalized Reed-Muller codes ⋮ On low weight codewords of generalized affine and projective Reed-Muller codes ⋮ On the fourth weight of generalized Reed-Muller codes ⋮ Relative generalized Hamming weights of evaluation codes ⋮ On the second Hamming weight of some Reed-Muller type codes ⋮ Highest numbers of points of hypersurfaces over finite fields and generalized Reed-Muller codes ⋮ Improved explicit estimates on the number of solutions of equations over a finite field ⋮ On the next-to-minimal weight of affine Cartesian codes ⋮ On the second weight of generalized Reed-Muller codes ⋮ Special numbers of rational points on hypersurfaces in the \(n\)-dimensional projective space over a finite field ⋮ On the third weight of generalized Reed-Muller codes

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