Abstract
今日量子力學在物理、數學、資訊等各種領域已經大量發展，而量子訊息理論已經是一門蓬勃發展的學科。如同錯誤更正碼在傳統的訊息理論中所佔據的地位，量子錯誤更正碼在量子訊息理論之中也扮演了一個不可或缺的角色。在量子錯碼更正碼的研究當中，量子穩定碼幾乎是最重要的一種編碼。量子穩定碼是和傳統線性碼相類似的一種量子碼，它的性質和編碼、解碼已經被廣泛的討論和深入的研究。在這篇論文裡，我們將會集中討論關於量子穩定碼的建構法，並且討論一些目前已知的量子穩定碼，關於其他的主題在此不會討論。首先，我們會介紹量子穩定碼的基本性質以及目前最實用且便利的建構法—Calderbank Shor Steane建構法，以及擴充Calderbank Shor Steane建構法。接下來我們將提出一種新的但是很簡單的想法，利用傳統的二元奇偶檢驗矩陣，我們可以得到一些量子穩定碼。此外，由這種建構法得到的量子穩定碼會具有額外增加的錯碼更正能力，可以修正一些額外的錯誤運算子。透過這個建構法，我們會利用傳統的里德-穆勒碼的二元奇偶檢驗矩陣來造出一系列的量子穩定碼。我們更進一步提出一個增加錯誤更正能力的方法，透過一種特殊的列的排列矩陣，這種量子穩定碼的最小距離可以增加一半。最後，我們特別討論了三種不同的量子循環碼。第一種量子循環碼是利用循環建構法得到的量子穩定碼，第二種是量子正交留數碼，第三種是量子的博斯-喬赫里-霍根漢碼。在最後的結論部分，我們會提出幾個未來研究思考的方向。

Abstract
Quantum information theory is a well-developed discipline today. Like classical
information theory, one central part of quantum information theory is
quantum error correction. In quantum coding theory, stabilizer codes are
probably the most important class of quantum codes. They are regarded as
the quantum analogue of the classical linear codes and the properties of stabilizer
codes have been carefully studied in the literature. In this thesis, we
focus on the construction of stabilizer codes and discuss some known quantum
codes. We will propose a new but simple perspective on construction by
classical parity-check matrices.

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