Linearly representable codes over chain rings

DOI10.1007/BF02940872zbMath0954.94019MaRDI QIDQ1969663

Thomas Honold, Ivan N. Landgev

Publication date: 19 March 2000

Published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (Search for Journal in Brave)

zbMATH Keywords

error correcting codechain ringprojective Hjelmslev geometry

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Combinatorial structures in finite projective spaces (51E20)

Related Items (10)

Isometric embeddings of \({\mathbb Z}_{p^k}\) in the Hamming space \({\mathbb F}_{p}^{N}\) and \({\mathbb Z}_{p^k}\)-linear codes ⋮ Few-weight codes from trace codes over a local ring ⋮ Non-free extensions of the simplex codes over a chain ring with four elements ⋮ Unnamed Item ⋮ On homogeneous arcs and linear codes over finite chain rings ⋮ 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 ⋮ Properties of codes with two homogeneous weights ⋮ On maximal arcs in projective Hjelmslev planes over chain rings of even characteristic ⋮ On linear codes over \(\mathbb Z_2\)

Uses Software

• Code Tables

Cites Work

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• On linear codes which attain the Solomon-Stiffler bound
• Hjelmslev-Räume. (Hjelmslev spaces)
• Codes and projective multisets
• A metric for codes over residue class rings
• Weighted modules and representations of codes
• Linear codes over finite chain rings
• Hjelmslev-Ebenen mit verfeinerten Nachbarschaftsrelationen
• Finite chain rings
• Kerdock code in a cyclic form
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• The Reed-Muller code R(r,m) is not Z/sub 4/-linear for 3≤r≤m-2
• Z/sub 2/k-linear codes
• Type II codes over F/sub 2/+uF/sub 2/
• All Reed-Muller codes are linearly representable over the ring of dual numbers over Z/sub 2/
• FINITE PRINCIPAL IDEAL RINGS
• On n-uniform Hjelmslev planes

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