New extremal binary self-dual codes of length 68 from generalized neighbors

DOI10.1016/j.ffa.2020.101727zbMath1465.94106arXiv2002.10030OpenAlexW3046379320MaRDI QIDQ1994939

Joe Gildea, Abidin Kaya, Adrian Korban, Bahattin Yildiz

Publication date: 18 February 2021

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

Full work available at URL: https://arxiv.org/abs/2002.10030

zbMATH Keywords

weight enumeratorextremal self-dual codesneighbor\(k\)th neighbordistance of self-dual codes

Mathematics Subject Classification ID

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

Related Items (5)

The weight enumerators of singly-even self-dual \([88,44,14\) codes and new binary self-dual \([68,34,12]\) and \([88,44,14]\) codes] ⋮ New extremal binary self-dual codes from block circulant matrices and block quadratic residue circulant matrices ⋮ Constructing self-dual codes from group rings and reverse circulant matrices ⋮ Composite matrices from group rings, composite \(G\)-codes and constructions of self-dual codes ⋮ New self-dual codes of length 68 from a \(2 \times 2\) block matrix construction and group rings

Uses Software

• Magma

Cites Work

• New extremal binary self-dual codes from a modified four circulant construction
• Various constructions for self-dual codes over rings and new binary self-dual codes
• The Magma algebra system. I: The user language
• Constructions for self-dual codes induced from group rings
• Modified quadratic residue constructions and new extremal binary self-dual codes of lengths 64, 66 and 68
• An altered four circulant construction for self-dual codes from group rings and new extremal binary self-dual codes. I
• Bordered constructions of self-dual codes from group rings and new extremal binary self-dual codes
• A new upper bound on the minimal distance of self-dual codes
• Weight enumerators of self-dual codes
• Some restrictions on weight enumerators of singly even self-dual codes
• Extremal binary self-dual codes
• Shadow bounds for self-dual codes
• Extremal self-dual codes with an automorphism of order 2
• New extremal singly even self-dual codes of lengths $64$ and $66$

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