{"paper":{"title":"Complete Weight Enumerators of Generalized Doubly-Even Self-Dual Codes","license":"","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.NT","authors_text":"E. M. Rains, Gabriele Nebe, H.-G. Quebbemann, N. J. A. Sloane","submitted_at":"2003-11-17T16:55:33Z","abstract_excerpt":"For any q which is a power of 2 we describe a finite subgroup of the group of invertible complex q by q matrices under which the complete weight enumerators of generalized doubly-even self-dual codes over the field with q elements are invariant.\n An explicit description of the invariant ring and some applications to extremality of such codes are obtained in the case q=4."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0311289","kind":"arxiv","version":1},"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"}