New extremal binary self-dual codes of length 66 as extensions of self-dual codes over \(R_k\)

DOI10.1016/j.jfranklin.2013.05.015zbMath1293.94112OpenAlexW2009125260MaRDI QIDQ396540

Bahattin Yildiz, Suat Karadeniz

Publication date: 13 August 2014

Published in: Journal of the Franklin Institute (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfranklin.2013.05.015

zbMATH Keywords

binary self-dual codes of parameters \([64,32,12\)]trivial automorphism groups

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Linear codes (general theory) (94B05)

Related Items

New extremal singly even self-dual codes of lengths $64$ and $66$ ⋮ New self-dual codes from \(2 \times 2\) block circulant matrices, group rings and neighbours of neighbours ⋮ New extremal binary self-dual codes from \(\mathbb{F}_4 + u \mathbb{F}_4\)-lifts of quadratic circulant codes over \(\mathbb{F}_4\) ⋮ New extremal binary self-dual codes from block circulant matrices and block quadratic residue circulant matrices ⋮ Codes over a family of local Frobenius rings, Gray maps and self-dual codes ⋮ Modified quadratic residue constructions and new extremal binary self-dual codes of lengths 64, 66 and 68

Uses Software

• Magma

Cites Work

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• Double-circulant and bordered-double-circulant constructions for self-dual codes over \(R_2\)
• Codes over \(R_k\), Gray maps and their binary images
• Self-dual codes over \(\mathbb F_2 + u\mathbb F_2 + v\mathbb F_2 + uv\mathbb F_2\)
• Linear codes over \({\mathbb{F}_2+u\mathbb{F}_2+v\mathbb{F}_2+uv\mathbb{F}_2}\)
• On binary self-dual codes of lengths 60, 62, 64 and 66 having an automorphism of order 9
• The Magma algebra system. I: The user language
• Classification of extremal double circulant self-dual codes of lengths 64 to 72
• Some optimal self-orthogonal and self-dual codes
• New extremal binary self-dual codes of length 64 from \(R_3\)-lifts of the extended binary Hamming code
• Extremal self-dual codes of length 64 through neighbors and covering radii
• A new upper bound on the minimal distance of self-dual codes
• Construction of Self-Dual Codes
• Extremal binary self-dual codes
• Extremal self-dual codes of lengths 66 and 68
• New extremal self-dual codes of lengths 36, 38, and 58
• Type II codes over F/sub 2/+uF/sub 2/
• On the classification and enumeration of self-dual codes