{"paper":{"title":"Stabilizer codes from modified symplectic form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"quant-ph","authors_text":"Piyush Kurur, Rajat Mittal, Tejas Gandhi","submitted_at":"2017-08-02T06:36:15Z","abstract_excerpt":"Stabilizer codes form an important class of quantum error correcting codes which have an elegant theory, efficient error detection, and many known examples. Constructing stabilizer codes of length $n$ is equivalent to constructing subspaces of $\\mathbb{F}_p^n \\times \\mathbb{F}_p^n$ which are \"isotropic\" under the symplectic bilinear form defined by $\\left\\langle (\\mathbf{a},\\mathbf{b}),(\\mathbf{c},\\mathbf{d}) \\right\\rangle = \\mathbf{a}^{\\mathrm{T}} \\mathbf{d} - \\mathbf{b}^{\\mathrm{T}} \\mathbf{c}$. As a result, many, but not all, ideas from the theory of classical error correction can be transl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00617","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"}