Self-dual codes over \(\mathbb Z_4[x]/(x^2 + 2x)\) and the \(\mathbb Z_4\)-images (Q1993395)

Summary: In this work, constructions for self-dual codes over the ring \(\mathbb Z_4[x]/(x^2 + 2x)\) are considered together with their images under an orthogonality-preserving Gray map, which result in self-dual \(\mathbb Z_4\)-codes. Theoretical results about the existence/non-existence of self-dual codes from construction methods such as the double circulant, bordered double circulant and four circulant matrices for the rings \(\mathbb Z_{4}\) and \(\mathbb Z_4[x]/(x^2 + 2x)\) are given. The construction methods are then applied to get good self-dual \(\mathbb Z_{4}\)-codes of lengths 16, 32, 48 and 64 (including some extremal type I and type II codes), which are tabulated at the end.