Cyclic codes over local Frobenius rings of order 16

DOI10.3934/amc.2017005zbMath1357.94091OpenAlexW2588763693MaRDI QIDQ514526

Abidin Kaya, Esengül Saltürk, Steven T. Dougherty

Publication date: 9 March 2017

Published in: Advances in Mathematics of Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/amc.2017005

zbMATH Keywords

cyclic codesGray mapscodes over local rings

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cyclic codes (94B15)

Related Items

Cyclic codes over \(\mathbb{F}_2 +u\mathbb{F}_2 +v\mathbb{F}_2 +v^2 \mathbb{F}_2\) with respect to the homogeneous weight and their applications to DNA codes ⋮ On cyclic codes over \(\mathbb{Z}_q [u / \langle u^2 \rangle\) and their enumeration] ⋮ Codes over a family of local Frobenius rings, Gray maps and self-dual codes ⋮ A note on constacyclic and quasi-cyclic codes over \({\mathbb{F}}_2+u{\mathbb{F}}_2+v{\mathbb{F}}_2+uv{\mathbb{F}}_2\) ⋮ Constacyclic codes over local rings of order 16 ⋮ Construction and enumeration for self-dual cyclic codes over \(\mathbb Z_4\) of oddly even length

Uses Software

• Code Tables

Cites Work

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• Codes over local rings of order 16 and binary codes
• Cyclic codes over \(R_{k}\)
• Cyclic codes over the integers modulo \(p^m\).
• Cyclic self-dual \(\mathbb Z_4\)-codes.
• Modular and \(p\)-adic cyclic codes
• On codes over Frobenius rings: generating characters, MacWilliams identities and generator matrices
• Cyclic codes over \({\mathbb{F}}_2 + u{\mathbb{F}}_2 + v{\mathbb{F}}_2 + uv{\mathbb{F}}_2\)
• Cyclic and Negacyclic Codes Over Finite Chain Rings
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• Negacyclic and cyclic codes over Z/sub 4/
• Cyclic codes and self-dual codes over F/sub 2/+uF/sub 2/

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