{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:DBF3NA5W4FGVVA53GU7TFNIISG","short_pith_number":"pith:DBF3NA5W","schema_version":"1.0","canonical_sha256":"184bb683b6e14d5a83bb353f32b508919eb75e7be21988e3f35535bd063d08a4","source":{"kind":"arxiv","id":"2506.23198","version":1},"attestation_state":"computed","paper":{"title":"Hybrid Character Sums From Vectorial Dual-Bent Functions and Asymptotically Optimal Complex Codebooks With Small Alphabet Sizes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chengju Li, Peng Wang, Ziling Heng","submitted_at":"2025-06-29T12:04:01Z","abstract_excerpt":"Hybrid character sums are an important class of exponential sums which have nice applications in coding theory and sequence design. Let $\\gf_{p^m}$ be the finite field with $p^m$ elements for a prime $p$ and a positive integer $m$. Let $V_n^{(p)}$ be an $n$-dimensional vector space over $\\gf_p$ for a prime $p$. In this paper, we study the hybrid character sums of the form \\begin{eqnarray*} \\sum_{x \\in V_n^{(p)}}\\psi\\left(F(x)\\right)\\chi_1\\left(a x\\right), \\end{eqnarray*} where $F$ is a function from $V_n^{(p)}$ to $\\gf_{p^m}$ and $a \\in V_n^{(p)}$, $\\psi$ is a nontrivial multiplicative charact"},"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":"2506.23198","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-06-29T12:04:01Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c9e2edcaea9fe7cdb58b5e459b9432855fa2085541c11e9f6a37ccbdacc66395","abstract_canon_sha256":"2b8b484ca87066851355f731da8fb5a7f5bb78fc659ab17dd65f9e620b842a6c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:29:17.556134Z","signature_b64":"RILCtPpsnrvEE2MvuT2XDlSOIaREvrz2kpnWNSpJyD7zYPTHnZiZiet28vVMFz3qL5LtAfDscMtinF3y4wX3AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"184bb683b6e14d5a83bb353f32b508919eb75e7be21988e3f35535bd063d08a4","last_reissued_at":"2026-07-05T11:29:17.555645Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:29:17.555645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hybrid Character Sums From Vectorial Dual-Bent Functions and Asymptotically Optimal Complex Codebooks With Small Alphabet Sizes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chengju Li, Peng Wang, Ziling Heng","submitted_at":"2025-06-29T12:04:01Z","abstract_excerpt":"Hybrid character sums are an important class of exponential sums which have nice applications in coding theory and sequence design. Let $\\gf_{p^m}$ be the finite field with $p^m$ elements for a prime $p$ and a positive integer $m$. Let $V_n^{(p)}$ be an $n$-dimensional vector space over $\\gf_p$ for a prime $p$. In this paper, we study the hybrid character sums of the form \\begin{eqnarray*} \\sum_{x \\in V_n^{(p)}}\\psi\\left(F(x)\\right)\\chi_1\\left(a x\\right), \\end{eqnarray*} where $F$ is a function from $V_n^{(p)}$ to $\\gf_{p^m}$ and $a \\in V_n^{(p)}$, $\\psi$ is a nontrivial multiplicative charact"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.23198","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.23198/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2506.23198","created_at":"2026-07-05T11:29:17.555699+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.23198v1","created_at":"2026-07-05T11:29:17.555699+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.23198","created_at":"2026-07-05T11:29:17.555699+00:00"},{"alias_kind":"pith_short_12","alias_value":"DBF3NA5W4FGV","created_at":"2026-07-05T11:29:17.555699+00:00"},{"alias_kind":"pith_short_16","alias_value":"DBF3NA5W4FGVVA53","created_at":"2026-07-05T11:29:17.555699+00:00"},{"alias_kind":"pith_short_8","alias_value":"DBF3NA5W","created_at":"2026-07-05T11:29:17.555699+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/DBF3NA5W4FGVVA53GU7TFNIISG","json":"https://pith.science/pith/DBF3NA5W4FGVVA53GU7TFNIISG.json","graph_json":"https://pith.science/api/pith-number/DBF3NA5W4FGVVA53GU7TFNIISG/graph.json","events_json":"https://pith.science/api/pith-number/DBF3NA5W4FGVVA53GU7TFNIISG/events.json","paper":"https://pith.science/paper/DBF3NA5W"},"agent_actions":{"view_html":"https://pith.science/pith/DBF3NA5W4FGVVA53GU7TFNIISG","download_json":"https://pith.science/pith/DBF3NA5W4FGVVA53GU7TFNIISG.json","view_paper":"https://pith.science/paper/DBF3NA5W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.23198&json=true","fetch_graph":"https://pith.science/api/pith-number/DBF3NA5W4FGVVA53GU7TFNIISG/graph.json","fetch_events":"https://pith.science/api/pith-number/DBF3NA5W4FGVVA53GU7TFNIISG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DBF3NA5W4FGVVA53GU7TFNIISG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DBF3NA5W4FGVVA53GU7TFNIISG/action/storage_attestation","attest_author":"https://pith.science/pith/DBF3NA5W4FGVVA53GU7TFNIISG/action/author_attestation","sign_citation":"https://pith.science/pith/DBF3NA5W4FGVVA53GU7TFNIISG/action/citation_signature","submit_replication":"https://pith.science/pith/DBF3NA5W4FGVVA53GU7TFNIISG/action/replication_record"}},"created_at":"2026-07-05T11:29:17.555699+00:00","updated_at":"2026-07-05T11:29:17.555699+00:00"}