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New binary self-dual codes via a generalization of the four circulant construction

Gildea, Joe
; 
Kaya, Abidin
; 
Yildiz, Bahattin
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University of Chester ; Sampoerna University ; Northern Arizona University
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2020-05-31
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Mathematics
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Abstract
In this work, we generalize the four circulant construction for self-dual codes. By applying the constructions over the alphabets $\mathbb{F}_2$, $\mathbb{F}_2+u\mathbb{F}_2$, $\mathbb{F}_4+u\mathbb{F}_4$, we were able to obtain extremal binary self-dual codes of lengths 40, 64 including new extremal binary self-dual codes of length 68. More precisely, 43 new extremal binary self-dual codes of length 68, with rare new parameters have been constructed.
Citation
Gildea, J., Abidin, K. & Bahattin, Y. (2020). New binary self-dual codes via a generalization of the four circulant construction. Mathematical Communications, 25, 213-226.
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Croatian Mathematical Society
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Mathematical Communications
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http://hdl.handle.net/10034/623408
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Article
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1848-8013
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