{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FJ224XHX53HTZARHGYBEDFTBII","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":"ddfe24a4b0a56d6c3e52e2eb7738eaf8266caff9aef8e0e5eb0b0912577a7c67","cross_cats_sorted":["math.IT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-12T23:30:21Z","title_canon_sha256":"c4d31c44897403892b7f08146ceafc295ad46fcc3ef45b114172c98be63f5b3e"},"schema_version":"1.0","source":{"id":"1604.03617","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.03617","created_at":"2026-05-18T00:13:55Z"},{"alias_kind":"arxiv_version","alias_value":"1604.03617v2","created_at":"2026-05-18T00:13:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03617","created_at":"2026-05-18T00:13:55Z"},{"alias_kind":"pith_short_12","alias_value":"FJ224XHX53HT","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FJ224XHX53HTZARH","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FJ224XHX","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:bfc4bcde511964de6e250e1258f8ad5074ffe50a892c32d7ab2e0547b7756dd0","target":"graph","created_at":"2026-05-18T00:13:55Z","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":"Let $\\mathbb{F}_q$ be a finite field with $q$ elements and denote by $\\theta : \\mathbb{F}_q\\to\\mathbb{F}_q$ an automorphism of $\\mathbb{F}_q$. In this paper, we deal with skew constacyclic codes, that is, linear codes of $\\mathbb{F}_q^n$ which are invariant under the action of a semi-linear map $\\Phi_{\\alpha,\\theta}:\\mathbb{F}_q^n\\to\\mathbb{F}_q^n$, defined by $\\Phi_{\\alpha,\\theta}(a_0,...,a_{n-2}, a_{n-1}):=(\\alpha \\theta(a_{n-1}),\\theta(a_0),...,\\theta(a_{n-2}))$ for some $\\alpha\\in\\mathbb{F}_q\\setminus\\{0\\}$ and $n\\geq 2$. In particular, we study some algebraic and geometric properties of t","authors_text":"Alexis E. Almendras Valdebenito, Andrea Luigi Tironi","cross_cats":["math.IT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-12T23:30:21Z","title":"A note on the duals of skew constacyclic codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03617","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:e0f27ffff863a0929562fded3a40c96e04d11ae932216e61c6f3ce63b101ff67","target":"record","created_at":"2026-05-18T00:13:55Z","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":"ddfe24a4b0a56d6c3e52e2eb7738eaf8266caff9aef8e0e5eb0b0912577a7c67","cross_cats_sorted":["math.IT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-04-12T23:30:21Z","title_canon_sha256":"c4d31c44897403892b7f08146ceafc295ad46fcc3ef45b114172c98be63f5b3e"},"schema_version":"1.0","source":{"id":"1604.03617","kind":"arxiv","version":2}},"canonical_sha256":"2a75ae5cf7eecf3c82273602419661420d3bcf110777a70cf5a933e8ae302979","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a75ae5cf7eecf3c82273602419661420d3bcf110777a70cf5a933e8ae302979","first_computed_at":"2026-05-18T00:13:55.431589Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:55.431589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2UwMpyavux0+LOFprRy9dlJ0sqtI5oucT/n7ZhgEaSZq/lSs2OyuQHlcx5uORZQzMLEIYtwmrxsJ6XIxFk2ABQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:55.432349Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.03617","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0f27ffff863a0929562fded3a40c96e04d11ae932216e61c6f3ce63b101ff67","sha256:bfc4bcde511964de6e250e1258f8ad5074ffe50a892c32d7ab2e0547b7756dd0"],"state_sha256":"f0348db273a0b84ea881121dc22292bf48c0ac13320fed785e4a58ace7c3d78d"}