Complementary Sequences - Golay Pair

Golay Pair

A complementary pair a, b may be encoded as polynomials A(z) = a(0) + a(1)z + ... + a(N − 1)zN−1 and similarly for B(z). The complementarity property of the sequences is equivalent to the condition

for all z on the unit circle, that is, |z| = 1. If so, A and B form a Golay pair of polynomials. Examples include the Shapiro polynomials, which give rise to complementary sequences of length a power of 2.