Obtaining quantum codes from classical linear codes

Although the capacities of the computers which are being used in daily life have been increased day by day, they are not enough to overcome some problems. For instance, while the problem of factoring a number to its primes is accomplished easily for small numbers, it takes months for higher numbers (like numbers with forty digits) even with the best computers. However, if succeeded, it is believed that a quantum computer can overcome the same problem within just a few minutes. Quantum error correcting codes have been developed in order to correct errors which can happen through transition of quantum information (qubit) in the quantum computers working with respect to principals of quantum mechanic. In the second section, some topics in algebra and classical coding which are needed to understand quantum coding are given. In the third section, some topics in linear algebra on Hilbert spaces which is studied in quantum coding, qubits which are units of quantum information, quantum logic gates and the conditions of error detection and correction for quantum codes are mentioned. In the fourth section, the structure of Calderbank-Shor-Steane codes and the parameters of quantum codes obtained from BCH codes are given. In the fifth section, the structure of stabilizer codes and the parameters of quantum codes obtained from classical codes which have control matrices satisfiying certain conditions are given