On determining the independent point set for doubly periodic arrays and encoding two-dimensional cyclic codes and their duals

For the purpose of encoding two-dimensional cyclic (TDC) codes, an effective algorithm for finding the independent point set of an arbitrary module of doubly periodic (DP) arrays is proposed. In addition, a method for determining the characteristic ideal of a given set of DP arrays is exhibited. With the aid of these methods it is possible to specify the structure of the generator and check ideals of TDC codes. By applying this algorithm to nonsemisimple binary TDC codes with small areas, several optimal linear codes have been found and their previously unknown TDC structures have been exhibited.