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Group LCD and group reversible LCD codes
Dougherty, Steven Gildea, Joe Korban, Adrian Roberts, Adam
Dougherty, Steven
Gildea, Joe
Korban, Adrian
Roberts, Adam
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EPub Date
Publication Date
2022-06-17
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Article - AAM
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Abstract
In this paper, we give a new method for constructing LCD codes. We employ group rings and a well known map that sends group ring elements to a subring of the
n
×
n
matrices to obtain LCD codes. Our construction method guarantees that our LCD codes are also group codes, namely, the codes are ideals in a group ring. We show that with a certain condition on the group ring element v, one can construct non-trivial group LCD codes. Moreover, we also show that by adding more constraints on the group ring element v, one can construct group LCD codes that are reversible. We present many examples of binary group LCD codes of which some are optimal and group reversible LCD codes with different parameters.
Citation
Dougherty, S. T., Gildea, J., Korban, A., & Roberts, A. M. (2022). Group LCD and group reversible LCD codes. Finite Fields and Their Applications, 83, 102079. https://doi.org/10.1016/j.ffa.2022.102079
Publisher
Elsevier
Journal
Finite Fields and Their Applications
Research Unit
DOI
10.1016/j.ffa.2022.102079
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PubMed Central ID
Type
Article
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Description
Series/Report no.
ISSN
1071-5797
EISSN
1090-2465