A Generalization Of The Lee Distance And Error Correcting Codes

In 1994 Huber found a way of using Gaussian integrals approach to construct two-dimensional signal . The so-called Mannheim weight constructed by Huber has such importance that it is able to correct one error. In [14], Huber applied his idea to Eisenstein integers;by means of a residue field ,he provided a two -dimensional express for any finite field.Later,in Cyclotomic field, Fan Yun, Gao Ying studied the subring consisting of algebric integers,see [15]. They are the first who regard any finite field as a residue field of the algebraic integer ring of a Cyclotomic field .Furthermore ,they introduce a Mannheim weight on a finite field;in addition, the given definition of the weight is quite different from the one given by Huber.In This paper,we first define Lee distance which is a generalization of the Lee distance and is defined over any finite field. Huber's Mannheim weight is a special case of ours. Finally ,we discuss the problems of constellations by generalization of the Lee distance.