Codes over rings and Hermitian lattices

DOI10.1007/s10623-014-9974-0zbMath1359.94688OpenAlexW2012229707MaRDI QIDQ494588

Jon-Lark Kim, Steven T. Dougherty, Yoon-Jin Lee

Publication date: 1 September 2015

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-014-9974-0

zbMATH Keywords

linear codeslatticesself-dual codesfinite ringsquadratic number fields

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05) Quadratic extensions (11R11) Lattices and convex bodies (number-theoretic aspects) (11H06)

Related Items (2)

Theta functions and symmetric weight enumerators for codes over imaginary quadratic fields ⋮ Theta series and weight enumerator over an imaginary quadratic field

Cites Work

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• Constructions of self-dual codes over finite commutative chain rings
• Self-dual codes over commutative Frobenius rings
• Codes over rings of size \(p^2\) and lattices over imaginary quadratic fields
• Inversive pseudorandom numbers over Galois rings
• Type II self-dual codes over finite rings and even unimodular lattices
• Applications of coding theory to the construction of modular lattices
• Duality for modules over finite rings and applications to coding theory
• Codes over $\mathbf {GF\pmb (4\pmb )}$ and $\mathbf {F}_2 \times \mathbf {F}_2$ and Hermitian lattices over imaginary quadratic fields
• Codes over rings of size four, Hermitian lattices, and corresponding theta functions

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