Construction of extremal self-dual codes over \(\mathbb F_2+u\mathbb F_2\) with an automorphism of odd order

DOI10.1016/j.ffa.2012.05.004zbMath1270.94068OpenAlexW1989151172MaRDI QIDQ714461

Hyun Jin Kim, Yoon-Jin Lee

Publication date: 11 October 2012

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

Full work available at URL: https://doi.org/10.1016/j.ffa.2012.05.004

zbMATH Keywords

self-dual codescodes over ringsGray mapextremal codesLee weightcodes with odd order automorphism

Mathematics Subject Classification ID

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

Related Items (5)

Hermitian self-dual codes over \(\mathbb F_{2^{2m}}+u\mathbb F_{2^{2m}}\) ⋮ Corrigendum to ``Construction of extremal self-dual codes over \(\mathbb F_2+u\mathbb F_2\) with an automorphism of odd order ⋮ Type I and Type II codes over the ring 𝔽2 + u𝔽2 + v𝔽2 + uv𝔽2 ⋮ Lee-extremal self-dual codes over \(\mathbb{F}_2 + u \mathbb{F}_2\) of lengths 23 and 24 ⋮ Type I and type II codes over the ring \(\mathbb{F}_2+s \mathbb{F}_2+s^2\mathbb{F}_2\)

Cites Work

• Construction of self-dual codes with an automorphism of order \(p\)
• Self-dual codes over \(\mathbb F_2 +u\mathbb F_2\) with an automorphism of odd order
• The existence of a self-dual \([70 ,35 ,12\) code and formally self-dual codes.]
• Euclidean and Hermitian self-dual MDS codes over large finite fields.
• Type II codes over \(\mathbb F_2+ u\mathbb F_2\) and applications to Hermitian modular forms
• On the decomposition of self-dual codes over \(\mathbb F_2 + u\mathbb F_2\) with an automorphism of odd prime order
• A linear construction for certain Kerdock and Preparata codes
• Type IV self-dual codes over rings
• Type II codes over F/sub 2/+uF/sub 2/
• Quaternary quadratic residue codes and unimodular lattices

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