Construction of punctured and extended quantum codes over GF(2)

On the basis of elementary transformation, we propose a new method for constructing a class of pure quantum codes [[n − i, 2k − n + i, d − i]]2 and [[n + 1, 2k − n − 1, d + 1]]2 from a class of classical linear codes [n, k, d]2 that contain their dual codes. The construction process was based on the elementary algebra; the error-correcting performance of the quantum codes was analyzed according to the relationship between the parity-check matrix and the minimum distance of the classical linear codes; the encoding and decoding networks were constructed based on the stabilizer. The proposed method is simple, straightforward and easy to implement using a computer and other hardware system. The theoretical results showed that the method is practical for the construction of a class of quantum codes.