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Podest\\'a","submitted_at":"2019-03-05T14:19:20Z","abstract_excerpt":"We consider cyclic codes $\\mathcal{C}_\\mathcal{L}$ associated to quadratic trace forms in $m$ variables $Q_R(x) = \\operatorname{Tr}_{q^m/q}(xR(x))$ determined by a family $\\mathcal{L}$ of $q$-linearized polynomials $R$ over $\\mathbb{F}_{q^m}$, and three related codes $\\mathcal{C}_{\\mathcal{L},0}$, $\\mathcal{C}_{\\mathcal{L},1}$ and $\\mathcal{C}_{\\mathcal{L},2}$. We describe the spectra for all these codes when $\\mathcal{L}$ is an even rank family, in terms of the distribution of ranks of the forms $Q_R$ in the family $\\mathcal{L}$, and we also compute the complete weight enumerator for $\\mathca"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1903.01838","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-05T14:19:20Z","cross_cats_sorted":[],"title_canon_sha256":"9564caaa3593ca3dfa530b583a18573ca3c6c9f379d1f612ace081cbd4b7f95a","abstract_canon_sha256":"d12f43536f1a8ba4b091e62a20f074f5b6d1ca3e59e8ba467077d31688ea86b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:49:07.278990Z","signature_b64":"RQykGHB6wSlM3B0VGaSg94wmZY6WEmHVKnELXIKNTY+C5BmqeqxGvOoCJAkdo93B/42naTVgAK+xIcIzBtH9AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50858110bd32970bffd44f1ec51de4fdef2fd9ab67de5f43d223bac51a7ca668","last_reissued_at":"2026-07-05T00:49:07.278613Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:49:07.278613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weight distribution of cyclic codes defined by quadratic forms and related curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Denis E. 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