Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the $k$-error linear complexity for $2^n$-periodic binary sequences
  via Cube Theory   The linear complexity and k-error linear complexity of a sequence have been
used as important measures of keystream strength, hence designing a sequence
with high linear complexity and $k$-error linear complexity is a popular
research topic in cryptography. In this paper, the concept of stable $k$-error
linear complexity is proposed to study sequences with stable and large
$k$-error linear complexity. In order to study k-error linear complexity of
binary sequences with period $2^n$, a new tool called cube theory is developed.
By using the cube theory, one can easily construct sequences with the maximum
stable $k$-error linear complexity. For such purpose, we first prove that a
binary sequence with period $2^n$ can be decomposed into some disjoint cubes
and further give a general decomposition approach. Second, it is proved that
the maximum $k$-error linear complexity is $2^n-(2^l-1)$ over all
$2^n$-periodic binary sequences, where $2^{l-1}\le k<2^{l}$. Thirdly, a
characterization is presented about the $t$th ($t>1$) decrease in the $k$-error
linear complexity for a $2^n$-periodic binary sequence $s$ and this is a
continuation of Kurosawa et al. recent work for the first decrease of k-error
linear complexity. Finally, A counting formula for $m$-cubes with the same
linear complexity is derived, which is equivalent to the counting formula for
$k$-error vectors. The counting formula of $2^n$-periodic binary sequences
which can be decomposed into more than one cube is also investigated, which
extends an important result by Etzion et al..

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The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc