{"paper":{"title":"New $q$-ary Quantum MDS Codes with Distances Bigger than $\\frac{q}{2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Hao Chen, Liqing Xu, Xianmang He","submitted_at":"2015-07-30T01:06:42Z","abstract_excerpt":"Constructions of quantum MDS codes have been studied by many authors. We refer to the table in page 1482 of [3] for known constructions. However there are only few $q$-ary quantum MDS $[[n,n-2d+2,d]]_q$ codes with minimum distances $d>\\frac{q}{2}$ for sparse lengths $n>q+1$. In the case $n=\\frac{q^2-1}{m}$ where $m|q+1$ or $m|q-1$ there are complete results. In the case $n=\\frac{q^2-1}{m}$ where $m|q^2-1$ is not a factor of $q-1$ or $q+1$, there is no $q$-ary quantum MDS code with $d> \\frac{q}{2}$ has been constructed. In this paper we propose a direct approch to construct Hermitian self-ortho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08355","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"}