Study On Quanternary Linear Codes

The theory of quaternary linear codes is one of the important subject of classical error-correcting coding theory in recent ten years,which is closely related with the study on constructions and properties of binary nonlinear codes.In this paper, we discuss the properties and the structure of the binary images of quaternary negacyclic codes. Moreover, we give a decoding algorithm for the general quaternary linear codes. Conclusions presented in this thesis can be summarized as follow:-A sufficient and necessary condition is given for the negacyclic odes whose binary images under the Gray map being cyclic, and some negacyclic codes whose binary images being cyclic are given by this condition. Moreover, the structure of the binary images are determined when they are cyclic over Z₂.-A decoding algorithm for general quaternary linear codes are presented by testing set,and the complexity of the algorithm are discussed.