On the code generated by the incidence matrix of points and \(k\)-spaces in \(\text{PG}(n,q)\) and its dual

DOI10.1016/j.ffa.2008.06.002zbMath1153.51006arXiv1201.3291OpenAlexW2217657927MaRDI QIDQ958614

Michel Lavrauw, Geertrui Van de Voorde, Storme, L.

Publication date: 5 December 2008

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

Full work available at URL: https://arxiv.org/abs/1201.3291

zbMATH Keywords

linear codesblocking setssmall weight codewordsdual of a codeProjective space

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Combinatorial aspects of finite geometries (05B25) Combinatorial structures in finite projective spaces (51E20) General block designs in finite geometry (51E05)

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The Use of Blocking Sets in Galois Geometries and in Related Research Areas ⋮ On low weight codewords of generalized affine and projective Reed-Muller codes ⋮ A Note on Small Weight Codewords of Projective Geometric Codes and on the Smallest Sets of Even Type ⋮ Large weight code words in projective space codes ⋮ Unique reducibility of multiple blocking sets ⋮ Tight sets in finite classical polar spaces ⋮ A small minimal blocking set in \(\mathrm{PG}(n,p^t)\), spanning a \((t-1)\)-space, is linear ⋮ Small weight codewords of projective geometric codes ⋮ On the code generated by the incidence matrix of points and \(k\)-spaces in \(\text{PG}(n,q)\) and its dual ⋮ A study of intersections of quadrics having applications on the small weight codewords of the functional codes \(C_2(Q)\), \(Q\) a non-singular quadric ⋮ Codes arising from incidence matrices of points and hyperplanes in \(\mathrm{PG}(n, q)\) ⋮ An empty interval in the spectrum of small weight codewords in the code from points and \(k\)-spaces of \(\mathrm{PG}(n,q)\) ⋮ Small weight codewords in the dual code of points and hyperplanes in PG\((n, q), q\) even

Cites Work

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• On the code generated by the incidence matrix of points and \(k\)-spaces in \(\text{PG}(n,q)\) and its dual
• On small blocking sets and their linearity
• The \(\mathbb{F}_p\) span of the incidence matrix of a finite projective plane
• Blocking sets in Desarguesian affine and projective planes
• Normal spreads
• Proper blocking sets in projective spaces
• Projective geometric codes
• Small point sets of PG\((2, q)\) intersecting each \(k\)-space in 1 modulo \(\sqrt q\) points
• A characterization of multiple (n – k)-blocking sets in projective spaces of square order
• A characterization of flat spaces in a finite geometry and the uniqueness of the hamming and the MacDonald codes
• Small blocking sets in higher dimensions

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