Two-dimensional cyclic codes of length $n=\ell s$ over the finite field $\mathbb{ F}$ are ideals of the polynomial ring $\frac{ \mathbb{ F}[x,y]}{ < x^{ s}-1,y^{ \ell}-1 >}$. The aim of this paper, is to present a novel method to study the algebraic structure of two-dimensional cyclic codes of any length $n=\ell s$ over the finite field $\mathbb{ F}$. By using this method, we find the generator polynomials for ideals of $\frac{ \mathbb{ F}[x,y]}{ < x^{ s}-1,y^{ \ell}-1 >}$ corresponding to two dimensional cyclic codes. These polynomials will be applied to obtain the generator matrix for two- dimensional cyclic codes.
Categories: math.AC