{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KFCGYRNEELNVACUAOHT5L5IBOJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a952c01c2465b71c1f046d2f1d2b5dc9bf08196a4cbe9c9974f190ec46be27f0","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.IT","submitted_at":"2015-05-02T17:09:47Z","title_canon_sha256":"0c934ef7e7c8fec513c08035cfb6be2a2ab8ad05276cc10219a18c91078a9c5c"},"schema_version":"1.0","source":{"id":"1505.00356","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00356","created_at":"2026-05-18T02:17:10Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00356v1","created_at":"2026-05-18T02:17:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00356","created_at":"2026-05-18T02:17:10Z"},{"alias_kind":"pith_short_12","alias_value":"KFCGYRNEELNV","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"KFCGYRNEELNVACUA","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"KFCGYRNE","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:b2b826313b50d7f97735c4d880ecdf836167212a0829b1b3832ffd557f0410b2","target":"graph","created_at":"2026-05-18T02:17:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we investigate the structure of repeated root constacyclic codes of length $2^amp^r$ over $\\mathbb{F}_{p^s}$ with $a\\geq1$ and $(m,p)=1$.\n  We characterize the codes in terms of their generator polynomials. This provides simple conditions on the existence of self-dual negacyclic codes. Further, we gave cases where the constacyclic codes are equivalent to cyclic codes.","authors_text":"Aicha Batoul, Kenza Guenda, T. Aaron Gulliver","cross_cats":["math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.IT","submitted_at":"2015-05-02T17:09:47Z","title":"On Repeated-Root Constacyclic Codes of Length $2^amp^r$ over Finite Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00356","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7caf3be312cc6ba82510bf8a762f6135dc981de7652ccbf538b961c533f1879a","target":"record","created_at":"2026-05-18T02:17:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a952c01c2465b71c1f046d2f1d2b5dc9bf08196a4cbe9c9974f190ec46be27f0","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.IT","submitted_at":"2015-05-02T17:09:47Z","title_canon_sha256":"0c934ef7e7c8fec513c08035cfb6be2a2ab8ad05276cc10219a18c91078a9c5c"},"schema_version":"1.0","source":{"id":"1505.00356","kind":"arxiv","version":1}},"canonical_sha256":"51446c45a422db500a8071e7d5f50172482494c747e46f3c7510783c51d332bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51446c45a422db500a8071e7d5f50172482494c747e46f3c7510783c51d332bb","first_computed_at":"2026-05-18T02:17:10.390201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:10.390201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wOCXOzVZojtQqUAQbPO4L0EvMdjyvabVkUuD6XexsOxBEhJGG7y9/SRzvfcLY5Atisi8Z/P+KDtJhHsPbyvyBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:10.390752Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.00356","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7caf3be312cc6ba82510bf8a762f6135dc981de7652ccbf538b961c533f1879a","sha256:b2b826313b50d7f97735c4d880ecdf836167212a0829b1b3832ffd557f0410b2"],"state_sha256":"a441e10a4035630cb0595fb2eeeabf958f6a5552a3cf3644e4a9250226bba436"}