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In this article, we study the following three classes of quadratic functions of wide interest. The class $\\mathcal{C}_1$ is defined for arbitrary $n$ as $\\mathcal{C}_1 = \\{Q(x) = Tr(\\sum_{i=1}^{\\lfloor (n-1)/2\\rfloor}a_ix^{2^i+1})\\;:\\; a_i \\in F_2\\}$, and the larger class $\\mathcal{C}_2$ is defined for even $n$ as $\\mathcal{C}_2 = \\{Q(x) = Tr(\\sum_{i=1}^{(n/2)-1}a_ix^{2^i+1}) +"},"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":"1603.04685","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-15T13:44:40Z","cross_cats_sorted":[],"title_canon_sha256":"338086c813225d3aecf6cee27763bde83183932c7237505be42e1a60835667e1","abstract_canon_sha256":"331a061982f7853829939601205e80d8612538d8107943c002732bed9c43fe54"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:04.189831Z","signature_b64":"XFV7znx+eQPeQrCeVXET9boE8BoIadDY2JnzmT1BR3Uc4ryHR2c2Eeu3sq4MSGt6r21zaWpBF5diLBAiXOZ2Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"500551088838a115ffc9a0c4dc1bc4580c400b71db4f640de229a6c40cb22277","last_reissued_at":"2026-05-18T01:19:04.189276Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:04.189276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Idempotent and p-potent quadratic functions: Distribution of nonlinearity and co-dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alev Topuzoglu, Nurdag\\\"ul Anbar, Wilfried Meidl","submitted_at":"2016-03-15T13:44:40Z","abstract_excerpt":"The Walsh transform $\\widehat{Q}$ of a quadratic function $Q:F_{p^n}\\rightarrow F_p$ satisfies $|\\widehat{Q}(b)| \\in \\{0,p^{\\frac{n+s}{2}}\\}$ for all $b\\in F_{p^n}$, where $0\\le s\\le n-1$ is an integer depending on $Q$. In this article, we study the following three classes of quadratic functions of wide interest. The class $\\mathcal{C}_1$ is defined for arbitrary $n$ as $\\mathcal{C}_1 = \\{Q(x) = Tr(\\sum_{i=1}^{\\lfloor (n-1)/2\\rfloor}a_ix^{2^i+1})\\;:\\; a_i \\in F_2\\}$, and the larger class $\\mathcal{C}_2$ is defined for even $n$ as $\\mathcal{C}_2 = \\{Q(x) = Tr(\\sum_{i=1}^{(n/2)-1}a_ix^{2^i+1}) +"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04685","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1603.04685","created_at":"2026-05-18T01:19:04.189344+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.04685v1","created_at":"2026-05-18T01:19:04.189344+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04685","created_at":"2026-05-18T01:19:04.189344+00:00"},{"alias_kind":"pith_short_12","alias_value":"KACVCCEIHCQR","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"KACVCCEIHCQRL76J","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"KACVCCEI","created_at":"2026-05-18T12:30:25.849896+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KACVCCEIHCQRL76JUDCNYG6ELA","json":"https://pith.science/pith/KACVCCEIHCQRL76JUDCNYG6ELA.json","graph_json":"https://pith.science/api/pith-number/KACVCCEIHCQRL76JUDCNYG6ELA/graph.json","events_json":"https://pith.science/api/pith-number/KACVCCEIHCQRL76JUDCNYG6ELA/events.json","paper":"https://pith.science/paper/KACVCCEI"},"agent_actions":{"view_html":"https://pith.science/pith/KACVCCEIHCQRL76JUDCNYG6ELA","download_json":"https://pith.science/pith/KACVCCEIHCQRL76JUDCNYG6ELA.json","view_paper":"https://pith.science/paper/KACVCCEI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.04685&json=true","fetch_graph":"https://pith.science/api/pith-number/KACVCCEIHCQRL76JUDCNYG6ELA/graph.json","fetch_events":"https://pith.science/api/pith-number/KACVCCEIHCQRL76JUDCNYG6ELA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KACVCCEIHCQRL76JUDCNYG6ELA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KACVCCEIHCQRL76JUDCNYG6ELA/action/storage_attestation","attest_author":"https://pith.science/pith/KACVCCEIHCQRL76JUDCNYG6ELA/action/author_attestation","sign_citation":"https://pith.science/pith/KACVCCEIHCQRL76JUDCNYG6ELA/action/citation_signature","submit_replication":"https://pith.science/pith/KACVCCEIHCQRL76JUDCNYG6ELA/action/replication_record"}},"created_at":"2026-05-18T01:19:04.189344+00:00","updated_at":"2026-05-18T01:19:04.189344+00:00"}