Abstract
In order to construct quantum error correction code, we consider additive codes over Galois field GF(4), which are self-orthogonal with respect to a certain Hermitian product. In this paper, we first propose a new approach to the construction of Hermitian self-orthogonal linear codes, applying the extension to get a longer length, and prove the codes have good minimum distance. Then, we investigate the corresponding quantum stabilizer codes from the classical codes. Six optimal quantum stabilizer codes have been achieved to show the effectiveness of the proposed construction.
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