{"paper":{"title":"Two new classes of quantum MDS codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Fang-Wei Fu, Weijun Fang","submitted_at":"2018-03-18T04:36:51Z","abstract_excerpt":"Let $p$ be a prime and let $q$ be a power of $p$. In this paper, by using generalized Reed-Solomon (GRS for short) codes and extended GRS codes, we construct two new classes of quantum maximum-distance- separable (MDS) codes with parameters \\[ [[tq, tq-2d+2, d]]_{q} \\] for any $1 \\leq t \\leq q, 2 \\leq d \\leq \\lfloor \\frac{tq+q-1}{q+1}\\rfloor+1$, and \\[ [[t(q+1)+2, t(q+1)-2d+4, d]]_{q} \\] for any $1 \\leq t \\leq q-1, 2 \\leq d \\leq t+2$ with $(p,t,d) \\neq (2, q-1, q)$. Our quantum codes have flexible parameters, and have minimum distances larger than $\\frac{q}{2}+1$ when $t > \\frac{q}{2}$. Furthe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06602","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"}