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Extremal binary self-dual codes from a bordered four circulant construction

Gildea, Joe
; 
Korban, Adrian
; 
Roberts, Adam
; 
Tylyshchak, Alexander
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Affiliation
Dundalk Institute of Technology; University of Chester; Ferenc Rakoczi II Transcarpathian Hungarian College of Higher Education
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Publication Date
2023-03-23
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Mathematics
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Abstract
In this paper, we present a new bordered construction for self-dual codes which employs λ-circulant matrices. We give the necessary conditions for our construction to produce self-dual codes over a finite commutative Frobenius ring of characteristic 2. Moreover, using our bordered construction together with the well-known building-up and neighbour methods, we construct many binary self-dual codes of lengths 56, 62, 78, 92 and 94 with parameters in their weight enumerators that were not known in the literature before.
Citation
Gildea, J., Korban, A., Roberts, A. M. & Tylyshchak, A. A. (2023). Extremal binary self-dual codes from a bordered four circulant construction. Discrete Mathematics, 346(8), article-number 113425. https://doi.org/10.1016/j.disc.2023.113425
Publisher
Elsevier
Journal
Discrete Mathematics
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URI
http://hdl.handle.net/10034/628971
DOI
10.1016/j.disc.2023.113425
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Article
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ISSN
0012-365X
EISSN
2578-9252
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https://www.sciencedirect.com/science/article/pii/S0012365X23001115?via%3Dihub
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