{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:XJZE4SVC222DDARARVSFRTKAZV","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":"bf13a608ac778114b36ebcc51e2a2bf7ab94ec0c99bf8ba1122e163b7d236246","cross_cats_sorted":["math.IT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-08-02T15:37:02Z","title_canon_sha256":"2c2747627261589021936e9e1013fb57a9de23b6a68977c22a043938c482f4ff"},"schema_version":"1.0","source":{"id":"1008.0327","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.0327","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"arxiv_version","alias_value":"1008.0327v2","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0327","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"pith_short_12","alias_value":"XJZE4SVC222D","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XJZE4SVC222DDARA","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XJZE4SVC","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:3a87ca5a11ca669f42894fe296a3c8c8a712ddb3a9a7443bfd4dd6ef40f01ef7","target":"graph","created_at":"2026-05-18T04:40:00Z","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":"Skew polynomial rings over finite fields ([7] and [10]) and over Galois rings ([8]) have been used to study codes. In this paper, we extend this concept to finite chain rings. Properties of skew constacyclic codes generated by monic right divisors of $x^n-\\lambda$, where $\\lambda$ is a unit element, are exhibited. When $\\lambda^2=1$, the generators of Euclidean and Hermitian dual codes of such codes are determined together with necessary and sufficient conditions for them to be Euclidean and Hermitian self-dual. Of more interest are codes over the ring $\\mathbb{F}_{p^m}+u\\mathbb{F}_{p^m}$. The","authors_text":"Patanee Udomkavanich, San Ling, Somphong Jitman","cross_cats":["math.IT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-08-02T15:37:02Z","title":"Skew Constacyclic Codes over Finite Chain Rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0327","kind":"arxiv","version":2},"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:c6adaed42b96971c40ad3a190c63dba437b01e39fa455f1f06d4664f646db78e","target":"record","created_at":"2026-05-18T04:40:00Z","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":"bf13a608ac778114b36ebcc51e2a2bf7ab94ec0c99bf8ba1122e163b7d236246","cross_cats_sorted":["math.IT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-08-02T15:37:02Z","title_canon_sha256":"2c2747627261589021936e9e1013fb57a9de23b6a68977c22a043938c482f4ff"},"schema_version":"1.0","source":{"id":"1008.0327","kind":"arxiv","version":2}},"canonical_sha256":"ba724e4aa2d6b43182208d6458cd40cd42495b10a3c292283bf4babf8948b0ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba724e4aa2d6b43182208d6458cd40cd42495b10a3c292283bf4babf8948b0ae","first_computed_at":"2026-05-18T04:40:00.478047Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:00.478047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DOdHPeg8wlnsKLHlO/xpdNN8c1bnm91xCs0D7nRGJBcTkNWq1TATjB6icAUlZdAGpaoE1U2MN1k3/8cqWZGdBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:00.478498Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.0327","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6adaed42b96971c40ad3a190c63dba437b01e39fa455f1f06d4664f646db78e","sha256:3a87ca5a11ca669f42894fe296a3c8c8a712ddb3a9a7443bfd4dd6ef40f01ef7"],"state_sha256":"c0ec5191dc69d38616958f88bc94d302b6b1d0676b5b01b6a700bc700f1d67af"}