Types of superregular matrices and the number of n‐arcs and complete n‐arcs in PG (r, q)
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Publication:5487773
DOI10.1002/jcd.20091zbMath1136.51008OpenAlexW1967457258MaRDI QIDQ5487773
Publication date: 12 September 2006
Published in: Journal of Combinatorial Designs (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/jcd.20091
Linear codes (general theory) (94B05) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Linear codes and caps in Galois spaces (51E22) Combinatorial aspects of finite geometries (05B25) Blocking sets, ovals, (k)-arcs (51E21)
Related Items (16)
Upper bounds on the smallest size of a complete arc in a finite Desarguesian projective plane based on computer search ⋮ Further results on the classification of MDS codes ⋮ Improved lower bounds on the domination number of hypercubes and binary codes with covering radius one ⋮ A construction of MDS 2D convolutional codes of rate \(1/n\) based on superregular matrices ⋮ New upper bounds on the smallest size of a complete arc in a finite Desarguesian projective plane ⋮ On the minimum size of complete arcs and minimal saturating sets in projective planes ⋮ On sizes of complete arcs in \(PG(2,q)\) ⋮ Extending small arcs to large arcs ⋮ A full classification of the complete k‐arcs of PG(2,23) and PG(2,25) ⋮ The Complete Arcs of PG(2,31) ⋮ Inclusion matrices and the MDS conjecture ⋮ The complete k-arcs of PG(2, 27) and PG(2, 29) ⋮ Special sequences as subcodes of Reed-Solomon codes ⋮ On sizes of complete caps in projective spaces \(\mathrm{PG}(n, q)\) and arcs in planes \(\mathrm{PG}(2, q)\) ⋮ New types of estimates for the smallest size of complete arcs in a finite Desarguesian projective plane ⋮ Upper bounds on the smallest size of a complete arc in \(\mathrm{PG}(2, {q})\) under a certain probabilistic conjecture
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