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The Golay complementary sequences have been studied for more than five decades since Golay first discovered those sequences. However, few studies on the correlation function of transformation form of q-ary complementary se- quences. New notions of equivalent transformation on q-ary sequences and equivalent transformation pair of a q-ary se- quence and its complex polyphase form are put forward. A theorem on equivalent transformations of q-ary sequences is proposed and proved. Two theorems of equivalent transformation pairs of a q-ary sequence and its complex polyphase form are presented and proved. Finally, Constructions of Golay complementary pairs based on the above theorems and examples are given. These new notions and new theorems are the basis for various constructions of Golay complementary pairs.

Equivalent Transformation Pairs of a q-ary Sequence and its Complex Polyphase Form and their Application