A natural generalization of two dimensional cyclic code ($\T{TDC}$) is two dimensional skew cyclic code. It is well-known that there is a correspondence between two dimensional skew cyclic codes and left ideals of the quotient ring $R_n:=\F[x,y;\rho,\theta]/<x^s-1, y^\ell-1>_l$. In this paper we characterize the left ideals of the ring $R_n$ with two methods and find the generator matrix for two dimensional skew cyclic codes.
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