On M.D.S. codes, arcs in PG(n,q) with q even, and a solution of three fundamental problems of B. Segre

DOI10.1007/BF01393742zbMath0654.94014OpenAlexW1974009707MaRDI QIDQ1109009

Aart Blokhuis, Joseph A. Thas, Aiden A. Bruen

Publication date: 1988

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143577

zbMATH Keywords

projective spacearcsMDS codesnormal rational curvemaximum distance separable code

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Combinatorial aspects of finite geometries (05B25) Combinatorial structures in finite projective spaces (51E20)

Related Items (24)

On the dual codes of skew constacyclic codes ⋮ On the uniqueness of (q + 1)-arcs of PG (5, q), q = 2_h, h ≥ 4 ⋮ Maximum distance separable codes and arcs in projective spaces ⋮ Contributions by Aart Blokhuis to finite geometry, discrete mathematics, and combinatorics ⋮ Diagonal groups and arcs over groups ⋮ Linear cutting blocking sets and minimal codes in the rank metric ⋮ The geometry of diagonal groups ⋮ Generalizing Erdős, Moon and Moser's result -- the number of \(k\)-dominating independent sets ⋮ Maximal AMDS codes ⋮ The basics of bases ⋮ On the Number ofk-Dominating Independent Sets ⋮ Some optimal codes from algebraic geometry and their covering radii ⋮ Polynomial multiplicities over finite fields and intersection sets ⋮ Bent vectorial functions and linear codes from o-polynomials ⋮ A construction for infinite families of semisymmetric graphs revealing their full automorphism group ⋮ Complete \(k\)-arcs in PG(\(n,q\)), \(q\) even ⋮ M.D.S. codes and arcs in \(\mathrm{PG}(n,q)\) with \(q\) even: an improvement of the bounds of Bruen, Thas, and Blokhuis ⋮ (6,3)-MDS codes over an alphabet of size 4 ⋮ Arcs and tensors ⋮ Open problems in finite projective spaces ⋮ Some generalizations of Rédei’s theorem ⋮ On the maximality of linear codes ⋮ Hyperplane sections of Grassmannians and the number of MDS linear codes ⋮ On the covering radius of Reed-Solomon codes

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• Curve razionali normali e \(k\)-archi negli spazi finiti
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• On the nonexistence of certain M.D.S. codes and projective planes
• The non-classical 10-arc of PG(4,9)
• Complete arcs and algebraic curves in \(\text{PG}(2,q)\)
• The solution to Beniamino Segre's problem \(I_ p,\),p=3, q=\(2^ k\).
• A combinatorial problem with applications to geometry
• On MDS extensions of generalized Reed- Solomon codes
• Maximum distance<tex>q</tex>-nary codes
• Orthogonal Arrays of Index Unity

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