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New binary self-dual codes of lengths 56, 58, 64, 80 and 92 from a modification of the four circulant construction.
Gildea, Joe Korban, Adrian Roberts, Adam
Gildea, Joe
Korban, Adrian
Roberts, Adam
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2021-05-31
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Abstract
In this work, we give a new technique for constructing self-dual codes over commutative Frobenius rings using $\lambda$-circulant matrices. The new construction was derived as a modification of the well-known four circulant construction of self-dual codes. Applying this technique together with the building-up construction, we construct singly-even binary self-dual codes
of lengths 56, 58, 64, 80 and 92 that were not known in the literature before. Singly-even self-dual codes of length 80 with $\beta \in \{2,4,5,6,8\}$ in their weight enumerators are constructed for the first time in the literature.
Citation
Gildea, J., Korban, A., & Roberts, A. (2021). New binary self-dual codes of lengths 56, 58, 64, 80 and 92 from a modification of the four circulant construction. Finite Fields and Their Applications, 75, 101876. https://doi.org/10.1016/j.ffa.2021.101876
Publisher
Elsevier
Journal
Finite Fields and Their Applications
Research Unit
DOI
10.1016/j.ffa.2021.101876
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Article
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This document is the Accepted Manuscript version of a published work that appeared in final form in Finite Fields and Their Applications. To access the final edited and published work see http://dx.doi.org/10.1016/j.ffa.2021.101876
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ISSN
1071-5797