Hyperplane sections of Grassmannians and the number of MDS linear codes

DOI10.1006/ffta.2000.0299zbMath1007.94024OpenAlexW1984633059MaRDI QIDQ1604408

Gilles Lachaud, Sudhir R. Ghorpade

Publication date: 4 July 2002

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

Full work available at URL: https://semanticscholar.org/paper/3fd56a83a725392ae430741ff6712998f5b786cd

zbMATH Keywords

Grassmannianhyperplane sectionMDS codeuniform matroidarcs in projective spaceGrassmann code

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Finite ground fields in algebraic geometry (14G15)

Related Items (18)

Enumerative coding for line polar Grassmannians with applications to codes ⋮ Arithmetic, Geometry, and Coding Theory: Homage to Gilles Lachaud ⋮ Number of solutions of systems of homogeneous polynomial equations over finite fields ⋮ On codes over \(\mathrm{FFN}(1,q)\)-projective varieties ⋮ Remarks on the Tsfasman-Boguslavsky Conjecture and higher weights of projective Reed-Muller codes ⋮ Generalizing Erdős, Moon and Moser's result -- the number of \(k\)-dominating independent sets ⋮ Counting generalized Reed-Solomon codes ⋮ Line polar Grassmann codes of orthogonal type ⋮ On the Number ofk-Dominating Independent Sets ⋮ Higher Grassmann codes ⋮ Schubert varieties, linear codes and enumerative combinatorics. ⋮ On Lagrangian-Grassmannian codes ⋮ Higher weights for the Lagrangian-Grassmannian codes ⋮ New strings for old Veneziano amplitudes. II: group-theoretic treatment ⋮ Decomposable subspaces, linear sections of Grassmann varieties, and higher weights of Grassmann codes ⋮ Codes on linear sections of the Grassmannian ⋮ Veneziano amplitudes, spin chains and abelian reduction of QCD ⋮ VENEZIANO AMPLITUDES, SPIN CHAINS, AND STRING MODELS

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