An Introduction to Golay Complementary Sequences

Abstract

First, I will discuss Golay sequences as Golay himself defined them, presenting his results on their lengths and his direct and recursive constructions. I will then discuss the broadest generalization yet defined, Golay array pairs. It is fruitful to understand complementary sequences as a special case of Golay array pairs, rather than Golay array pairs simply as an extension of the more fundamental complementary sequences. First, I will discuss their basic properties, and then the ways in which they can be transformed into higher or lower dimensional arrays. Secondly, within the context of Golay array pairs, I will discuss the other main generalizations and developments, beginning with Jedwab and Davis’ non-recursive structure, which led to the division of standard and non-standard Golay sequences, both of which I will discuss. Thirdly, I will present the basic extensions of Golay sequences: Golay sets, and multiple L-shift complementary sequences.