{"paper":{"title":"LDPC Codes Based on the Space of Symmetric Matrices over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Changli Ma, Meng Zhao, Qi Wang","submitted_at":"2016-05-24T02:54:48Z","abstract_excerpt":"In this paper, we present a new method for explicitly constructing regular low-density parity-check (LDPC) codes based on $\\mathbb{S}_{n}(\\mathbb{F}_{q})$, the space of $n\\times n$ symmetric matrices over $\\mathbb{F}_{q}$. Using this method, we obtain two classes of binary LDPC codes, $\\cal{C}(n,q)$ and $\\cal{C}^{T}(n,q)$, both of which have grith $8$. Then both the minimum distance and the stopping distance of each class are investigated. It is shown that the minimum distance and the stopping distance of $\\cal{C}^{T}(n,q)$ are both $2q$. As for $\\cal{C}(n,q)$, we determine the minimum distanc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07273","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"}