Research On Two Classes Of Linear Codes Over Finite Rings

Since the theory of error-correcting codes on finite rings has become a hot topic coding theory, various of finite rings are studied by scholars. Particularly, the finding that classical self-orthogonal codes can be used to construct quantum error-correcting codes is really significant in communication. Since then, the construction of classical self-orthogonal codes has been received extensively.In this thesis, cyclic self-orthogonal codes on ring Zp2 and additive negacyclic codes on ring Z2Z4 are mainly studied. The specific research is as below:On the one hand, firstly, an introduction of the basic knowledge about cyclic codes and self-orthogonal codes is given. Then, generator polynomial of cyclic self-orthogonal codes on ring Zp2 and the generator polynomial of its self-dual codes are mainly discussed. Finally, a sufficient and necessary condition for the existence and amount of cyclic self-orthogonal codes on ring Zp2are obtained. In particular, the form and amount of cyclic self-dual codes on ring Zp 2 are determined.On the other hand, the relevant concepts of additive negacyclic codes on ring Z2Z4 are firstly introduced. Then the structures of additive negacyclic codes of odd length and any length are given. And finally, minimal spanning sets of additive negacyclic codes on ring Z2Z4 are provided.