{"paper":{"title":"Constructing an LDPC Code Containing a Given Vector","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Martin Bossert, Sven M\\\"uelich, Sven Puchinger","submitted_at":"2017-03-23T09:13:26Z","abstract_excerpt":"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 $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07973","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}