Z4(Z4+vZ4)-linear and consta cyclic codes

The thesis contains of five sections. In the first section, basic definitions and theorems about algebra and coding theory are given. The basic problem of coding theory is explained and today,ıts main idea,extending to polar code construction, has been discussed. It is emphasized that additive codes are used in the quantum error correction process. In addition, literature research for single error correcting hamming code is mentioned.In the second section, the structure of the linear code Z4(Z4+vZ4) where v^2=1 is introduced.In the third section, cyclic codes over Z4Z4[v] , v^2=1 is investigated. Cyclic codes over this ring are investigated and the general form of the generator and a minimal spanning set of such codes are determined.Also new gray map are defined and gray images of some cyclic codes are examined.In the fourth section, constacyclic codes over Z4R- where v^2=1 for R=Z4+vZ4 are studied. New gray map is defined and gray images is determined.In the fifth section, the algebraic structure of the ring Z4R1, v^2=2 and R1=Z4+vZ4 is examined. Z4R1-Constacycle codes have been studied, new and different gray map have been defined and their images have been examined. In the last section, the conclusion and some recommendations are given Keywords: Linear codes,cyclic codes,constacyclic codes, additive codes.