Constructing an LDPC Code Containing a Given Vector

Abstract

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 Müelich 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).

5 pages, accepted at the International Workshop on Algebraic and Combinatorial Coding Theory, 2018

References in corpus (1)

• A New Error Correction Scheme for Physical Unclonable Functions