On the second weight of generalized Reed-Muller codes
From MaRDI portal
Publication:1009052
DOI10.1007/s10623-008-9211-9zbMath1196.94091OpenAlexW2166286240MaRDI QIDQ1009052
Publication date: 31 March 2009
Published in: Designs, Codes and Cryptography (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10623-008-9211-9
Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Varieties over finite and local fields (11G25)
Related Items (25)
Direct products in projective Segre codes ⋮ The second weight of generalized Reed-Muller codes in most cases ⋮ Minimum distance functions of graded ideals and Reed-Muller-type codes ⋮ 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 ⋮ The second and the third smallest arrangements of hyperplanes in finite projective spaces ⋮ Regularity index of the generalized minimum distance function ⋮ On the next-to-minimal weight of projective Reed-Muller codes ⋮ Relative generalized Hamming weights of evaluation codes ⋮ On the codewords of generalized Reed-Muller codes reaching the fourth weight ⋮ On the second Hamming weight of some Reed-Muller type codes ⋮ On Zeros of a Polynomial in a Finite Grid ⋮ Minimum distance functions of complete intersections ⋮ On the Alon-Füredi bound ⋮ Completing the determination of the next-to-minimal weights of affine cartesian codes ⋮ On the bounds and achievability about the ODPC of \(\mathrm{GRM}(2,m)^*\) over prime fields for increasing message length ⋮ Generalized minimum distance functions ⋮ Footprint and minimum distance functions ⋮ Generalized Hamming weights of projective Reed-Muller-type codes over graphs ⋮ On the next-to-minimal weight of affine Cartesian codes ⋮ Maximum number of \(\mathbb{F}_q\)-rational points on nonsingular threefolds in \(\mathbb{P}^4\) ⋮ High dimensional affine codes whose square has a designed minimum distance ⋮ Contemporary coding theory. Abstracts from the workshop held March 17--23, 2019 ⋮ On the third weight of generalized Reed-Muller codes
Cites Work
- On the number of points of some hypersurfaces in \(\mathbb{F}^n_q\)
- On codes from norm-trace curves
- Second highest number of points of hypersurfaces in \(\mathbb F_q^n\)
- New generalizations of the Reed-Muller codes--I: Primitive codes
- On generalized ReedMuller codes and their relatives
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: On the second weight of generalized Reed-Muller codes
