Self-dual codes and quadratic residue codes over the ring   $\mathbb{Z}_9+u\mathbb{Z}_9$
  In this paper, we introduce a new definitions of the Gray weight and the Gray map for linear codes over $\mathbb{Z}_9+u\mathbb{Z}_9$ with $u^2=u$. Some results on self-dual codes over this ring are investigated. Further, the structural properties of quadratic residue codes are also considered. Two self-dual codes with parameters $[22,11,5]$ and $[24,12,9]$ over $\mathbb{Z}_9$ are obtained. 
Jian Gao, XianFang Wang, Fang-Wei Fu
cs.IT math.IT math.RA