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:
“The works of women are symbolical.
We sew, sew, prick our fingers, dull our sight,
Producing what? A pair of slippers, sir,
To put on when you’re weary or a stool
To stumble over and vex you ... “curse that stool!”
Or else at best, a cushion, where you lean
And sleep, and dream of something we are not,
But would be for your sake. Alas, alas!
This hurts most, this ... that, after all, we are paid
The worth of our work, perhaps.”
—Elizabeth Barrett Browning (1806–1861)