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We also give the structure of $\\lambda$-constacyclic codes of length $p^sm$ with $\\lambda=\\alpha_1+u\\alpha_2+...+u^{e-1} \\alpha_{e-1}$, where $\\alpha_1,\\alpha_2 \\neq 0$ and study the self-duality of these codes."},"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":"1211.7326","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.IT","submitted_at":"2012-11-30T17:52:30Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"00d66f4b28dac5b2dae731522832c4fad790fe718f766aa0d2edbb813371d71d","abstract_canon_sha256":"4eb6728af111a35f5ecd6a7365a28f49c8175b6a3644727061902d4bfe606d9a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:30.933011Z","signature_b64":"ef+meka2o2HurSlFp4PK8F3OdNaDvQEuGapm0L2sEj+AQPe1AVGpFs5ZHBhvKP7ZCHjiru03F41nTk6DL/b/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"897ffa2fa32d9d917b58b7f5059a0b9711acd0ee7f792f892b42dae8d5d674f5","last_reissued_at":"2026-05-18T03:39:30.932360Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:30.932360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Repeated Root Constacyclic Codes of Length $mp^s$ over $\\mathbb{F}_{p^r}+u \\mathbb{F}_{p^r}+...+ u^{e-1}\\mathbb{F}_{p^r}$","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Kenza Guenda, T. 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