{"paper":{"title":"On tensor products of CSS Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT","quant-ph"],"primary_cat":"cs.IT","authors_text":"Alain Couvreur, Benjamin Audoux","submitted_at":"2015-12-22T13:37:23Z","abstract_excerpt":"CSS codes are in one-to-one correspondance with length 3 chain complexes. The latter are naturally endowed with a tensor product $\\otimes$ which induces a similar operation on the former. We investigate this operation, and in particular its behavior with regard to minimum distances. Given a CSS code $\\mathcal{C}$, we give a criterion which provides a lower bound on the minimum distance of $\\mathcal{C} \\otimes \\mathcal{D}$ for every CSS code $\\mathcal D$. We apply this result to study the behaviour of iterated tensor powers of codes. Such sequences of codes are logarithmically LDPC and we prove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07081","kind":"arxiv","version":3},"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"}