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For any $\\omega\\in R^\\times$ and positive integers $k, n$ satisfying ${\\rm gcd}(p,n)=1$, we prove that any $(1+\\omega u)$-constacyclic code of length $p^kn$ over $R$ is monomially equivalent to a matrix-product code of a nested sequence of $p^k$ cyclic codes with length $n$ over $R$ and a $p^k\\times p^k$ matrix $A_{p^k}$ over $\\mathbb{F}_p$. Using the matrix-product structures, we give an iterative construction o"},"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":"1803.01095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-03-03T02:50:16Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"8faa5bb7b61c177cdfdd22a72d02096b92226d9537de39a45c482c1d82a7ca05","abstract_canon_sha256":"0d9c8ab7dbe2c8c103c9b2826769bedc3a48b1a69032db58377481ecaf470d68"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:01.783275Z","signature_b64":"fgxlbj33FxAbMOnJqH+g553TKb2CY1dJ6W62loatF9Ok3P0JQ+/jnT0TDiCmsJKlxvDmQ82pR0xoRUOfKYgFCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2cb90d40840c988b6825411e15dab6b479ee4cdd6b06cf0d4123b0168baec6ff","last_reissued_at":"2026-05-18T00:22:01.782739Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:01.782739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Matrix-product structure of constacyclic codes over finite chain rings $\\mathbb{F}_{p^m}[u]/\\langle u^e\\rangle$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Fang-Wei Fu, Yonglin Cao, Yuan Cao","submitted_at":"2018-03-03T02:50:16Z","abstract_excerpt":"Let $m,e$ be positive integers, $p$ a prime number, $\\mathbb{F}_{p^m}$ be a finite field of $p^m$ elements and $R=\\mathbb{F}_{p^m}[u]/\\langle u^e\\rangle$ which is a finite chain ring. For any $\\omega\\in R^\\times$ and positive integers $k, n$ satisfying ${\\rm gcd}(p,n)=1$, we prove that any $(1+\\omega u)$-constacyclic code of length $p^kn$ over $R$ is monomially equivalent to a matrix-product code of a nested sequence of $p^k$ cyclic codes with length $n$ over $R$ and a $p^k\\times p^k$ matrix $A_{p^k}$ over $\\mathbb{F}_p$. 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