Self-dual codes over Z_4[x]/(x~2+2x) and the Z_4-images

摘要

In this work, constructions for self-dual codes over the ring Z_(4)[ x ]/( x ~(2) + 2 x ) are considered together with their images under an orthogonality-preserving grey map, which result in self-dual Z4-codes. Theoretical results about the existenceon-existence of self-dual codes from construction methods such as the double circulant, bordered double circulant and four circulant matrices for the rings Z_(4) and Z_(4)[ x ]/( x ~(2) + 2 x ) are given. The construction methods are then applied to get good self-dual 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.