Self-orthogonal codes over \(\mathbb{Z}_4\) arising from the chain ring \(\mathbb{Z}_4 [u] / \langle u^2 + 1 \rangle \)

DOI10.1016/j.ffa.2021.101972zbMath1485.94159OpenAlexW3217175902MaRDI QIDQ2066398

Boran Kim, Nayoung Han, Yoon-Jin Lee

Publication date: 14 January 2022

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2021.101972

zbMATH Keywords

optimal codeadditive codeGray mapself-orthogonal codechain ring

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05)

Uses Software

• Z4 database

Cites Work

• Constructions of self-dual codes over finite commutative chain rings
• Self-dual codes over commutative Frobenius rings
• Construction of MDS self-dual codes over Galois rings
• Construction of extremal Type II codes over \(\mathbb{Z}_4\).
• Euclidean and Hermitian self-dual MDS codes over large finite fields.
• A mass formula for cyclic codes over Galois rings of characteristic \(p^3\)
• Additive codes over Galois rings
• Additive perfect codes in Doob graphs
• Algebraic structure of additive conjucyclic codes over \(\mathbb{F}_4\)
• Classification of cyclic codes over a non-Galois chain ring \(\mathbb{Z}_p [u / \langle u^3 \rangle\)]
• A method for constructing self-dual codes over \(\mathbb {Z}_{2^m}\)
• Lee weights of cyclic self-dual codes over Galois rings of characteristic \(p^2\)
• CONSTRUCTION OF SELF-DUAL CODES OVER F₂+ uF₂
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• New extremal self-dual codes of lengths 36, 38, and 58
• Quantum error correction via codes over GF(4)
• Cyclic codes and self-dual codes over F/sub 2/+uF/sub 2/
• AN EFFICIENT CONSTRUCTION OF SELF-DUAL CODES

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