Constructing self-dual codes from group rings and reverse circulant matrices (Q2025380)

A self-dual code is a code which satisfies \(C=C^\perp.\) The authors give a construction for self-dual codes over rings of characteristic \(2\) using group rings and reverse circulant matrices. They apply it to rings that are equipped with a gray map to the binary space to construct binary self-dual codes. By applying extension and neighbor constructions along with this method, they construct \(3\) new codes of length \(64,\) \(22\) of length \(68,\) \(12\) of length \(80,\) and \(4\) of length \(92\).