Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sequence Pairs with Lowest Combined Autocorrelation and Crosscorrelation   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.

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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: adap-org