Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Autocorrelations of Binary Sequences and Run Structure   We analyze the connection between the autocorrelation of a binary sequence
and its run structure given by the run length encoding. We show that both the
periodic and the aperiodic autocorrelation of a binary sequence can be
formulated in terms of the run structure. The run structure is given by the
consecutive runs of the sequence. Let C=(C(0), C(1),...,C(n)) denote the
autocorrelation vector of a binary sequence. We prove that the kth component of
the second order difference operator of C can be directly calculated by using
the consecutive runs of total length k. In particular this shows that the kth
autocorrelation is already determined by all consecutive runs of total length
L<k. In the aperiodic case we show how the run vector R can be efficiently
calculated and give a characterization of skew-symmetric sequences in terms of
their run length encoding.

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The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th