Linear Codes over Finite Chain Rings and Projective Hjelmslev Geometries

DOI10.1142/9789812837691_0003zbMath1196.94092OpenAlexW2323854193MaRDI QIDQ3645839

Thomas Honold, Ivan N. Landgev

Publication date: 18 November 2009

Published in: Codes Over Rings (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/9789812837691_0003

zbMATH Keywords

arclinear codesweight enumeratorblocking setsWitt vectorfinite chain ringsprojective Hjelmslev geometry

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Linear codes and caps in Galois spaces (51E22) Combinatorial aspects of finite geometries (05B25) Blocking sets, ovals, (k)-arcs (51E21) Ring geometry (Hjelmslev, Barbilian, etc.) (51C05)

Related Items (11)

Unnamed Item ⋮ Unnamed Item ⋮ On the rank of incidence matrices in projective Hjelmslev spaces ⋮ Non-free extensions of the simplex codes over a chain ring with four elements ⋮ New ring-linear codes from dualization in projective Hjelmslev geometries ⋮ Unnamed Item ⋮ The maximal size of 6- and 7-arcs in projective Hjelmslev planes over chain rings of order 9 ⋮ The existence of maximal \((q^2,2)\)-arcs in projective Hjelmslev planes over chain rings of length 2 and odd prime characteristic ⋮ Conditions for the existence of spreads in projective Hjelmslev spaces ⋮ Blocking sets of Rédei type in projective Hjelmslev planes ⋮ A Griesmer bound for linear codes over finite quasi-Frobenius rings

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