A class of cyclic Codes Over the Ring ${\mathbb{Z}}_4[u]\mathrm{/}<u^2>$ and its Gray image

Cyclic codes over R have been introduced recently. In this paper, we study the cyclic codes over R and their ${\mathbb{Z}}_2$ image. Making use of algebraic structure, we find the some good ${\mathbb{Z}}_2$ codes of length 28.