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New Extremal Binary Self-dual Codes from block circulant matrices and block quadratic residue circulant matrices
Gildea, Joe Kaya, Abidin Taylor, Rhian Tylyshchak, Alexander Yildiz, Bahattin
Gildea, Joe
Kaya, Abidin
Taylor, Rhian
Tylyshchak, Alexander
Yildiz, Bahattin
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2021-08-20
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Abstract
In this paper, we construct self-dual codes from a construction that involves both block circulant matrices and block quadratic residue circulant matrices. We provide conditions when this construction can yield self-dual codes. We construct self-dual codes of various lengths over F2 and F2 + uF2. Using extensions, neighbours and sequences of neighbours, we construct many new self-dual codes. In particular, we construct one new self-dual code of length 66 and 51 new self-dual codes of length 68.
Citation
Gildea, J., Kaya, A., Taylor, R., Tylyshchak, A., & Yildiz, B. (2021). New extremal binary self-dual codes from block circulant matrices and block quadratic residue circulant matrices. Discrete Mathematics, 344(11), 112590. https://doi.org/10.1016/j.disc.2021.112590
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Elsevier
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Discrete Mathematics
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0012-365X