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.
Read more about this topic: Complementary Sequences
Famous quotes containing the word pair:
“Firm-style bean curd insoles cushion feet, absorb perspiration and provide more protein than meat or fish innersoles of twice the weight. Tofu compresses with use, becoming more pungent and flavorful. May be removed when not in use to dry or marinate. Innersoles are ready to eat after 1,200 miles of wear. Each pair provides adult protein requirement for 2 meals. Insoles are sized large to allow for snacks. Recipe booklet included.”
—Alfred Gingold, U.S. humorist. Items From Our Catalogue, “Tofu Innersoles,” Avon Books (1982)