Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A lower bound on the 2-adic complexity of modified Jacobi sequence   Let $p,q$ be distinct primes satisfying $\mathrm{gcd}(p-1,q-1)=d$ and let
$D_i$, $i=0,1,\cdots,d-1$, be Whiteman's generalized cyclotomic classes with
$Z_{pq}^{\ast}=\cup_{i=0}^{d-1}D_i$. In this paper, we give the values of Gauss
periods based on the generalized cyclotomic sets
$D_0^{\ast}=\sum_{i=0}^{\frac{d}{2}-1}D_{2i}$ and
$D_1^{\ast}=\sum_{i=0}^{\frac{d}{2}-1}D_{2i+1}$. As an application, we
determine a lower bound on the 2-adic complexity of modified Jacobi sequence.
Our result shows that the 2-adic complexity of modified Jacobi sequence is at
least $pq-p-q-1$ with period $N=pq$. This indicates that the 2-adic complexity
of modified Jacobi sequence is large enough to resist the attack of the
rational approximation algorithm (RAA) for feedback with carry shift registers
(FCSRs).

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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas