How Do More Golay Sequences Arise?

In 1999, Davis and Jedwab gave a direct construction of Golay complementary sequences over Zopf <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sup> of length 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> . Recently, Li and Chu found 1024 more quaternary Golay complementary sequences of length 16, that cannot be obtained by the direct construction, using exhaustive computer enumeration. It is shown how these sequences arise from interleaving and concatenation of two classes of Golay complementary sequences given as an example by Davis and Jedwab. These examples spawn new Golay sequences over Zopf <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2 </sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sup> of length 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> for all h ges 2 and m ges 4