The Construction Of Two-Dimensional Error-Correcting Codes

Current memory devices require that information is stored on two-dimensional surfaces. Up until now, one-dimensional codes have been used for such applications by folding the one-dimensional data into the two-dimensional surface. The main disadvantage of this ap-proach is that the devices are not capable of handling "real" two dimensional error patterns. So it has higher bounds on the redundancy. Recently experts lie more and more attention on two-dimensional error-correcting codes.In this paper,2-cluster-correcting codes are constructed for three connectivity model: +,* and * type on the two-dimensional surface respectively. Moreover, the codes are shown to meet sphere-packing bound, and to be optimal. Since the codes in the paper are linear, a quite simple decoding algorithms can be designed for them by the way of choosing a basis. Finally, the decoding algorithms are also been presented in the paper.