Cyclic codes over some rings

In this thesis, the structure and relations of cyclic codes over special rings and cyclic codes over fields are investigated. In the first chapter of the thesis, the beginning and progress of Coding Theory and the contents of the studies that shaped the thesis in this field are mentioned. In the second chapter, basic algebraic information is given for Coding Theory, linear codes, and especially cyclic codes. In the third chapter, the structure of cyclic codes on two variable rings with coefficients in 2 with conditions 2 u u = , 2 v = 0 , uv vu = = 0 and structure of codes corresponding to their Gray images are studied. Similarly, different codes are obtained with a different ring structure in the 2 u =1 condition. Moreover, a new transform was written on the field 3 under the same conditions, and new codes are obtained. In the last chapter of the thesis, the structure of rings with two variable coefficients in 3 and 5 under conditions 2 u u − , 2 v , uv , vu , and Gray images are examined. Keywords: Linear Codes, Cyclic Codes, Gray Maps, Codes over the Rings.