  In this paper, we study skew cyclic codes with arbitrary length over the ring
$R=\mathbb{F}_{p}+u\mathbb{F}_{p}$ where $p$ is an odd prime and $% u^{2}=0$.
We characterize all skew cyclic codes of length $n$ as left $% R[x;\theta
]$-submodules of $R_{n}=R[x;\theta ]/\langle x^{n}-1\rangle $. We find all
generator polynomials for these codes and describe their minimal spanning sets.
Moreover, an encoding and decoding algorithm is presented for skew cyclic codes
over the ring $R$. Finally, based on the theory we developed in this paper, we
provide examples of codes with good parameters over $F_{p}$ with different odd
prime $p.$ In fact, example 25 in our paper is a new ternary code in the class
of quasi-twisted codes. The other examples we provided are examples of optimal
codes.
