1. Codes over GF(4) Polynomials can be used and their transformations as shown here

2. Codes over GF(4) and Pauli Matrices

4. From Symplectic Form to GF(4)

5. Self Orthogonal & Self Dual

6. Toric Codes of Kitaev 1997

8. Toric Code Example

11. Homological Codes

15. Conclusions Reliable quantum computation can not be achieved without error control. Quantum error correcting codes were discovered in 1995 by breaking the barrier of quantum no-cloning theorem. Quantum error correction is a challenging, interesting, and rich field for research.

16. References