A combinatorial construction of the Gray map over Galois rings

DOI10.1016/j.disc.2008.09.002zbMath1183.94061OpenAlexW2048771505MaRDI QIDQ1025970

Bahattin Yildiz

Publication date: 23 June 2009

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2008.09.002

zbMATH Keywords

Galois ringslinear codesaffine geometriesGray mapshomogeneous weightsaffine hyperplanes

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27)

Related Items

Linear codes over \(\mathbb {F}_{q}[x/(x^2)\) and \(\mathrm{GR}(p^2,m)\) reaching the Griesmer bound] ⋮ Normal bases on Galois ring extensions

Cites Work

• A metric for codes over residue class rings
• Homogeneous weights and exponential sums.
• Codes over \(\mathbb F_{3} + u\mathbb F_{3}\) and improvements to the bounds on ternary linear codes
• Weights modulo \(p^e\) of linear codes over rings
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• Decompositions and extremal type II codes over Z/sub 4/
• Gray isometries for finite chain rings and a nonlinear ternary (36, 3/sup 12/, 15) code
• Z(p/sup k+1/)-linear codes
• Z/sub 2/k-linear codes
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