{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:ORXNBLYPARHROMEZNAQHYMXOGW","short_pith_number":"pith:ORXNBLYP","schema_version":"1.0","canonical_sha256":"746ed0af0f044f17309968207c32ee35a87e6b4d9d4b690be765d847ef1dbce5","source":{"kind":"arxiv","id":"1906.09542","version":1},"attestation_state":"computed","paper":{"title":"New Optimal $Z$-Complementary Code Sets from Matrices of Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Shibsankar Das, Sudhan Majhi, Udaya Parampalli, Zilong Liu","submitted_at":"2019-06-23T02:45:50Z","abstract_excerpt":"The concept of paraunitary (PU) matrices arose in the early 1990s in the study of multi-rate filter banks. So far, these matrices have found wide applications in cryptography, digital signal processing, and wireless communications. Existing PU matrices are subject to certain constraints on their existence and hence their availability is not guaranteed in practice. Motivated by this, for the first time, we introduce a novel concept, called $Z$-paraunitary (ZPU) matrix, whose orthogonality is defined over a matrix of polynomials with identical degree not necessarily taking the maximum value. We "},"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":"1906.09542","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-06-23T02:45:50Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ba78f3b96e64580464a1fe8fe4f211e42f62e33765224c9a90758a4046ac09a2","abstract_canon_sha256":"e4dc62de95f72b0dd2370ac05ea68372a122e3f409009a65938fcab85a6b7b3c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:37.640722Z","signature_b64":"U43lWJqBM/yX/6TrA4MsZxAIshEBLcdbvVDt4fKwRoJT12CXbvqE8ghfHpcjqUMmZd2wPPhYYf9yFumJmUkIBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"746ed0af0f044f17309968207c32ee35a87e6b4d9d4b690be765d847ef1dbce5","last_reissued_at":"2026-05-17T23:42:37.639964Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:37.639964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New Optimal $Z$-Complementary Code Sets from Matrices of Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Shibsankar Das, Sudhan Majhi, Udaya Parampalli, Zilong Liu","submitted_at":"2019-06-23T02:45:50Z","abstract_excerpt":"The concept of paraunitary (PU) matrices arose in the early 1990s in the study of multi-rate filter banks. So far, these matrices have found wide applications in cryptography, digital signal processing, and wireless communications. Existing PU matrices are subject to certain constraints on their existence and hence their availability is not guaranteed in practice. Motivated by this, for the first time, we introduce a novel concept, called $Z$-paraunitary (ZPU) matrix, whose orthogonality is defined over a matrix of polynomials with identical degree not necessarily taking the maximum value. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09542","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":"1906.09542","created_at":"2026-05-17T23:42:37.640079+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.09542v1","created_at":"2026-05-17T23:42:37.640079+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09542","created_at":"2026-05-17T23:42:37.640079+00:00"},{"alias_kind":"pith_short_12","alias_value":"ORXNBLYPARHR","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"ORXNBLYPARHROMEZ","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"ORXNBLYP","created_at":"2026-05-18T12:33:24.271573+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/ORXNBLYPARHROMEZNAQHYMXOGW","json":"https://pith.science/pith/ORXNBLYPARHROMEZNAQHYMXOGW.json","graph_json":"https://pith.science/api/pith-number/ORXNBLYPARHROMEZNAQHYMXOGW/graph.json","events_json":"https://pith.science/api/pith-number/ORXNBLYPARHROMEZNAQHYMXOGW/events.json","paper":"https://pith.science/paper/ORXNBLYP"},"agent_actions":{"view_html":"https://pith.science/pith/ORXNBLYPARHROMEZNAQHYMXOGW","download_json":"https://pith.science/pith/ORXNBLYPARHROMEZNAQHYMXOGW.json","view_paper":"https://pith.science/paper/ORXNBLYP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.09542&json=true","fetch_graph":"https://pith.science/api/pith-number/ORXNBLYPARHROMEZNAQHYMXOGW/graph.json","fetch_events":"https://pith.science/api/pith-number/ORXNBLYPARHROMEZNAQHYMXOGW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ORXNBLYPARHROMEZNAQHYMXOGW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ORXNBLYPARHROMEZNAQHYMXOGW/action/storage_attestation","attest_author":"https://pith.science/pith/ORXNBLYPARHROMEZNAQHYMXOGW/action/author_attestation","sign_citation":"https://pith.science/pith/ORXNBLYPARHROMEZNAQHYMXOGW/action/citation_signature","submit_replication":"https://pith.science/pith/ORXNBLYPARHROMEZNAQHYMXOGW/action/replication_record"}},"created_at":"2026-05-17T23:42:37.640079+00:00","updated_at":"2026-05-17T23:42:37.640079+00:00"}