Pursley and Sarwate established a lower bound on a combined measure of autocorrelation and crosscorrelation for a pair $(f,g)$ of binary sequences (i.e., sequences with terms in $\{-1,1\}$). If $f$ is a nonzero sequence, then its autocorrelation demerit factor, $\text{ADF}(f)$, is the sum of the squared magnitudes of the aperiodic autocorrelation values over all nonzero shifts for the sequence obtained by normalizing $f$ to have unit Euclidean norm. If $(f,g)$ is a pair of nonzero sequences, then their crosscorrelation demerit factor, $\text{CDF}(f,g)$, is the sum of the squared magnitudes of the aperiodic crosscorrelation values over all shifts for the sequences obtained by normalizing both $f$ and $g$ to have unit Euclidean norm. Pursley and Sarwate showed that for binary sequences, the sum of $\text{CDF}(f,g)$ and the geometric mean of $\text{ADF}(f)$ and $\text{ADF}{(g)}$ must be at least $1$. For randomly selected pairs of long binary sequences, this quantity is typically around $2$. In this paper, we show that Pursley and Sarwate's bound is met for binary sequences precisely when $(f,g)$ is a Golay complementary pair. We also prove a generalization of this result for sequences whose terms are arbitrary complex numbers. We investigate constructions that produce infinite families of Golay complementary pairs, and compute the asymptotic values of autocorrelation and crosscorrelation demerit factors for such families.

翻译：Pursley 和 Sarwate 在对一对二进制序列的一对美元(f) 美元(g) 和二进制序列(即以$+1,1美元为条件的顺序)。如果美元是一个非零序列,那么其自动通缩贬值系数 $\ text{ADF}(f) 是所有非零变化的周期性美元自动通缩值之和。 美元(f) 是美元(f) 和美元(g) 通过对美元(f) 进行正常化以形成单位的 Euclidean 规范而获得的顺序。 如果美元(f) 是非零序列的一对, 那么它们的二进制交易因数, $(text) 和 美元(f) (f) 美元(f) 定期通缩缩缩缩成数的平值之和所有变化的正数之和。 美元(wesley) 和 Sarwatelery(r) 以美元(r) 美元(r) 和美元(rf) 美元(rexf) 美元(rex) 美元) 的直成序的直序为正数。