  Generalized quasi-cyclic (GQC) codes with arbitrary lengths over the ring
$\mathbb{F}_{q}+u\mathbb{F}_{q}$, where $u^2=0$, $q=p^n$, $n$ a positive
integer and $p$ a prime number, are investigated. By the Chinese Remainder
Theorem, structural properties and the decomposition of GQC codes are given.
For 1-generator GQC codes, minimal generating sets and lower bounds on the
minimum distance are given. As a special class of GQC codes, quasi-cyclic (QC)
codes over $\mathbb{F}_q+u\mathbb{F}_q$ are also discussed briefly in this
paper.
