Skew cyclic codes over some finite rings and quantum codes

Linear codes have a significant role on constructing quantum error-correcting codes. In this thesis, we study skew cyclic codes over some finite rings. As an application, we construct quantum codes from skew cyclic codes. This thesis consists of five chapters. Chapter 1 includes the main problem of the coding theory and the summary of the literature review are included. The basic definitions and the fundamental theorems of abstract algebra and algebraic coding theory are given in Chapter 2. Chapter 3 consists of the properties of the ring $R=F_q[u]\big/(u^{k+1}-u)$ and the skew polynomial ring. In this chapter, the properties of linear codes and skew cyclic codes over $R$ are explained. Quantum codes over $F_q$ are constructed from skew cyclic codes over $R$ in Chapter 4. In the fifth chapter, the discussion and the conclusion about the subject of the thesis are given.