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For any $\\alpha,\\beta\\in \\mathbb{F}_{p^m}^{\\times}$, the aim of this paper is to represent all distinct $(\\alpha+u\\beta)$-constacyclic codes over $R$ of length $p^sn$ and their dual codes, where $s$ is a nonnegative integer and $n$ is a positive integer satisfying ${\\rm gcd}(p,n)=1$. Especially, all distinct $(2+u)$-constacyclic codes of length $6\\cdot 5^t$ over $\\mathbb{F}_{3}+u\\mathb"},"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":"1511.02743","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-11-09T16:24:22Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d52fbf44a38838a77b09c3e4f2afd4d945b996db640f941a251f09443d3529c0","abstract_canon_sha256":"d70626e7d5960c7c843f9a85b1732c829c7865d1811ff514c124e8f0754dfe2d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:21.830092Z","signature_b64":"WPo9rtLKS6MY6lEVlSKLhYKcd4Bm5kZ2vgVcd3QGkikqMKIVTlJcozate4I/n44kmLn5JhmAOtNxNy6NYhhNDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ad97a7f33703237bd0e611e7f0872a7952864094d62763e3d8adeacce871f3b","last_reissued_at":"2026-05-18T01:27:21.829640Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:21.829640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On $(\\alpha+u\\beta)$-constacyclic codes of length $p^sn$ over $\\mathbb{F}_{p^m}+u\\mathbb{F}_{p^m}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Qingguo Li, Yuan Cao","submitted_at":"2015-11-09T16:24:22Z","abstract_excerpt":"Let $\\mathbb{F}_{p^m}$ be a finite field of cardinality $p^m$ and $R=\\mathbb{F}_{p^m}[u]/\\langle u^2\\rangle=\\mathbb{F}_{p^m}+u\\mathbb{F}_{p^m}$ $(u^2=0)$, where $p$ is an odd prime and $m$ is a positive integer. For any $\\alpha,\\beta\\in \\mathbb{F}_{p^m}^{\\times}$, the aim of this paper is to represent all distinct $(\\alpha+u\\beta)$-constacyclic codes over $R$ of length $p^sn$ and their dual codes, where $s$ is a nonnegative integer and $n$ is a positive integer satisfying ${\\rm gcd}(p,n)=1$. 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