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Skew cyclic codes of lengthp s overF pm +uF pm.Iranian Journal of Science and Technology, Transactions A: Science, 46(5):1469–1475, 2022","work_id":"4c9492cf-00cf-429d-aeb7-069272b81df7","year":2022},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"D. Boucher and F. Ulmer. Linear codes using skew polynomials with automorphisms and derivations.Designs, Codes and Cryptography. An International Journal, 70:405– 431, 2014","work_id":"ab7c7a0d-9852-45c6-a5a5-53aa75bd9231","year":2014},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"B. Boudine and J. Laaouine. Polycyclic codes over Fpm[u] ⟨u2⟩ : Classification, hamming distance, and annihilators.Finite Fields and Their Applications, 88:102188, 2023. 18","work_id":"1003136a-8908-4828-bbcf-8b7ac5c53651","year":2023},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"B. Boudine, J. Laaouine, and M. E. Charkani. On the classification of ideals over R[x]/⟨f(x) ps ⟩whenR=F pm +uF pm +. . .+u nFpm.Cryptography and Communica- tions, 15(3):589–598, 2023","work_id":"c16b07f0-435b-4d0d-93c3-6c1613c86690","year":2023},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"M. Boulagouaz and A. Leroy. (σ, δ)-codes.Advances in Mathematics of Communications, 7(4):463–474, 2013","work_id":"ba9ccb7a-8af6-4fac-9557-cc9a82e6e646","year":2013}],"snapshot_sha256":"ef58bf451cc47e43fbddb32d3db94cda6399ea00970704f2db6105fe5a76e25e"},"source":{"id":"2605.13020","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-14T18:25:52.968815Z","id":"576d55ee-c5d5-41ae-992c-44e16f88dd64","model_set":{"reader":"grok-4.3"},"one_line_summary":"Skew polycyclic codes over the chain ring R^t are the left ideals of the quotient skew polynomial ring, with explicit structural descriptions and generators provided for central f(x) of the form x^{np^s} - lambda when n=1 or 2, plus complete listings for n=1 t=3 and n=2 t=2 that correct prior gaps.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The structure of left ideals in skew polynomial rings over finite chain rings is refined for central elements x^{np^s} - λ with nonzero constant term.","strongest_claim":"For n=1,t=3 and n=2,t=2 we give a full description of the left ideals by including certain necessary conditions that were omitted in available literature, preventing the different classes of left ideals from being mutually disjoint and in certain cases, we also compute i-th torsion codes.","weakest_assumption":"The automorphism Θ of R^t extends the automorphism θ of F_{p^m} with Θ(u)=u, and λ_0 ≠ 0 for the central element f(x) = x^{np^s} - λ."}},"verdict_id":"576d55ee-c5d5-41ae-992c-44e16f88dd64"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ac8ba9a5a167e526e91ffc32b3b7a8dd8da9228be5a1526f2c07217c9e529d52","target":"record","created_at":"2026-05-18T03:09:00Z","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":"229b3c6f63fb9a5d0844b4b86055a3d78cbe47c1d902649f64ad7e96e48df126","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IT","submitted_at":"2026-05-13T05:24:15Z","title_canon_sha256":"3e413130beb47536fb011285130160d0cf50056b2b38bdcf9ea0486d3a93a63a"},"schema_version":"1.0","source":{"id":"2605.13020","kind":"arxiv","version":1}},"canonical_sha256":"6530d615514f082e2eb2386158d28361c5c7fce4543db9e470aa2a864e6087bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6530d615514f082e2eb2386158d28361c5c7fce4543db9e470aa2a864e6087bc","first_computed_at":"2026-05-18T03:09:00.048791Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:00.048791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MxRleODe3FYd0GSowEeSp1iAUAERJX3ZyHdsvZRKdX4rFQJ1/HXcpy6gRptSpE5cOT8D8u1e8GmmdmJqZWhWBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:00.049296Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13020","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac8ba9a5a167e526e91ffc32b3b7a8dd8da9228be5a1526f2c07217c9e529d52","sha256:c12ec197f5791ee9628463f5c11b1078e8eccc89d9fe414d5a746f3aa958382d"],"state_sha256":"f0c38009bd56d06dedbb5bd43d58d107cab1e0ca9e16634b1e614480bdc65f41"}