在此篇論文中，我們提出了利用已知的格雷互補對，來建構格雷互補集合的新方法。不同於現有的文獻只能加入至多三個位元，並由現有的序列以及其互補配對來組合出格雷互補集合。在我們的方法中，序列集合的長度可以很有彈性地調整。與目前的文獻中建構方法相比，我們是第一個提出可以加入一至六個位元的建構方法。而用來建構出格雷互補集合的格雷互補對也不需要採用其互補配對。除此之外，我們也提出了由完全互補碼建構格雷互補集合的建構法。藉由這兩個方式所建構出來的格雷互補集合，其尖峰平均功率比具有理論上界。對於我們提出的建構方法，產生的序列可以補足一些過去文獻中沒有的序列長度，也更加提高了在實際系統上應用的可能性。

In this thesis, new constructions of Golay complementary set (GCSs) are proposed based on Golay complementary pair (GCP). Via adding one to six bits at the beginning or at the end of two GCPs, the generated GCS has larger set size and longer sequence length. Compared to previous results in the literature, our methods are constructions with more bits added to GCPs. The sequence length is very flexible. Compared with previous methods, this thesis is the first work to propose constructions of GCSs width more available lengths. Furthermore, we propose constructions of GCSs based on concatenated complete complementary codes (CCCs) and GCPs. The flexible sequence lengths and set size of our constructed GCSs will increase more possible applications in practical systems.

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