AuthorsDougherty, Steven T.
Korban, Adrian; orcid: 0000-0001-5206-6480
Roberts, Adam M.; orcid: 0000-0002-0654-7096
MetadataShow full item record
AbstractIn 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.
CitationFinite Fields and Their Applications, volume 83, page 102079
DescriptionFrom Elsevier via Jisc Publications Router
History: accepted 2022-06-03, epub 2022-06-17, issued 2022-10-31
Article version: AM
Publication status: Published