A Note On Sequence Folding

Multidimensional coding attracts a lot of attention in the last three decades,one of the main reasons is their modern applications. Some memory devices, suchas page-oriented optical memories, etc., require that information is stored on atwo-dimensional surface and two-dimensional error patterns occored in storingmust be recovered.Folding a sequence into a multidimensional box is an important techniquein multidimensional coding. Etzion [22] generalizes this technique by a latticetilling for a given shape, and shows that all previous known folding defnitionsare special cases of this new defnition. In this paper we give a new interpreationto this defnition from the point-view of algebra, and discuss the existence of afolding. Necessary and sufcient conditions for the existence of a folding are alsopresented.In Ref [21], Schwartz and Etzion constructed some optimal or nearly optimal2cluster error-correcting codes for three types error models, respectively, andpresented a class of3cluster error-correcting codes for the criss-cross connec-tivity whose redundancies have three bits more than the sphere-packing bound.In this paper a class of nearly optimal3cluster error-correcting codes are con-structed, the encoding algorithm and the decoding algorithm of these codes arealso presented.