Linear Code And Association Scheme

Coding theory plays an important role in the communication, and some properties of codesare obtained the attention by the specialist. Association schemes have close connections withcoding theory、graph theory and finite fields theory, and in particular, provide a framework forstudying codes and designs. The research work on association scheme theory has tremendoussense.In this paper, we use the important conclusion for linear code studied by Delsarte in[1]:if C is a linear code with s weights,then the restriction to C of the Hamming scheme is anassociation scheme with s classes if and only if among the coset of ist dual code C⊥exactlys+1distinct weight distributions occur.From other conclusions, we have known that the weightdistributions of the linear code’ coset have relation to the weights of its dual code.Up to equivalence of codes, for linear code of two dimension this paper introduces thegeneral form of the linear code’ generator matrix for the one, two, three-weight codes, and forthe linear code of two-weight, introduces a necessary and sufficient condition that the restrictionto C of the Hamming association scheme is itself an association scheme.