Self-dual codes over Z<SUB align="right">4[<i>x</i>]/(<i>x</i><SUP align="right">2</SUP> + 2<i>x</i>) and the Z<SUB align="right">4-images

Abstract

In this work, constructions for self-dual codes over the ring Z4[x]/(x2 + 2x) are considered together with their images under an orthogonality-preserving grey map, which result in self-dual Z4-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 Z4 and Z4[x]/(x2 + 2x) are given. The construction methods are then applied to get good self-dual Z4-codes of lengths 16, 32, 48 and 64 (including some extremal type I and type II codes), which are tabulated at the end.