Research on LDPC codes is in the ascendant nowadays.Our paper has done some work on the proposition of "performance of different codes in the same family constrained by weight distribution polynomials".Different codes of the same weight distribution are listed

and the results indicate the upper performance is determined by density evolution theory and the lower performance limit by the Fill-Shift construction method.Furthermore

the codes in the collection of elementary matrix transformation share the same error-correction performance but different coding complexity.We can get a conclusion that codes constrained by weight distribution polynomial can be divided into many groups

performance among different groups is not the same

it depends on the loops length and distribution

and performance in the same groups is identical.What we can do now is that to find the best group and do suitable transformations if given weight distribution polynomials.Through this paper

we can see that a new idea for code constructing is also presented.If the relations between big girth of LDPC codes and weight distribution polynomial are discovered

new codes can be achieved only by the weight distribution polynomial

the currently used method given in references for code constructing will be less useful.We can think that we have found a completely different method to construct LDPC codes.