, Volume 56, Issue 3, pp 1-11
Date: 09 Nov 2012

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

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Abstract

On the basis of elementary transformation, we propose a new method for constructing a class of pure quantum codes [[ni, 2kn + i, d − i]]2 and [[n + 1, 2kn − 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.