Constructing an LDPC Code Containing a Given Vector
The coding problem considered in this work is to construct a linear code $\mathcal{C}$ of given length $n$ and dimension $k
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| creator | Müelich, Sven Puchinger, Sven Bossert, Martin |
| description | The coding problem considered in this work is to construct a linear code
$\mathcal{C}$ of given length $n$ and dimension $k |
| doi_str_mv | 10.48550/arxiv.1703.07973 |
| format | Article |
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$\mathcal{C}$ of given length $n$ and dimension $k<n$ such that a given binary
vector $\mathbf{r} \in \mathbb{F}^{n}$ is contained in the code. We study a
recent solution of this problem by M\"uelich and Bossert, which is based on
LDPC codes. We address two open questions of this construction. First, we show
that under certain assumptions, this code construction is possible with high
probability if $\mathbf{r}$ is chosen uniformly at random. Second, we calculate
the uncertainty of $\mathbf{r}$ given the constructed code $\mathcal{C}$. We
present an application of this problem in the field of Physical Unclonable
Functions (PUFs).</description><identifier>DOI: 10.48550/arxiv.1703.07973</identifier><language>eng</language><subject>Computer Science - Information Theory ; Mathematics - Information Theory</subject><creationdate>2017-03</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1703.07973$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1703.07973$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Müelich, Sven</creatorcontrib><creatorcontrib>Puchinger, Sven</creatorcontrib><creatorcontrib>Bossert, Martin</creatorcontrib><title>Constructing an LDPC Code Containing a Given Vector</title><description>The coding problem considered in this work is to construct a linear code
$\mathcal{C}$ of given length $n$ and dimension $k<n$ such that a given binary
vector $\mathbf{r} \in \mathbb{F}^{n}$ is contained in the code. We study a
recent solution of this problem by M\"uelich and Bossert, which is based on
LDPC codes. We address two open questions of this construction. First, we show
that under certain assumptions, this code construction is possible with high
probability if $\mathbf{r}$ is chosen uniformly at random. Second, we calculate
the uncertainty of $\mathbf{r}$ given the constructed code $\mathcal{C}$. We
present an application of this problem in the field of Physical Unclonable
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$\mathcal{C}$ of given length $n$ and dimension $k<n$ such that a given binary
vector $\mathbf{r} \in \mathbb{F}^{n}$ is contained in the code. We study a
recent solution of this problem by M\"uelich and Bossert, which is based on
LDPC codes. We address two open questions of this construction. First, we show
that under certain assumptions, this code construction is possible with high
probability if $\mathbf{r}$ is chosen uniformly at random. Second, we calculate
the uncertainty of $\mathbf{r}$ given the constructed code $\mathcal{C}$. We
present an application of this problem in the field of Physical Unclonable
Functions (PUFs).</abstract><doi>10.48550/arxiv.1703.07973</doi><oa>free_for_read</oa></addata></record> |
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| identifier | DOI: 10.48550/arxiv.1703.07973 |
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| subjects | Computer Science - Information Theory Mathematics - Information Theory |
| title | Constructing an LDPC Code Containing a Given Vector |
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