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Let $D={\\bf F}_q\\backslash\\{a_1,\\ldots,a_l\\}$ and $k$ be an integer such that $2\\le k\\le q-l-1$. In this paper, we study the deep holes of generalized projective Reed-Solomon code ${\\rm GPRS}_q(D, k)$ of length $q-l+1$ and dimension $k$ over ${\\bf F}_q$. For any $f(x)\\in {\\bf F}_q[x]$, we let $f(D)=(f(y_1),\\ldots,f(y_{q-l}))$ if "},"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":"1705.07823","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-05-22T15:59:48Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"e24ac51a02ccb6f7ccc02ca98b83d73eabe84c51edaf4ec7da08566d4d0553c0","abstract_canon_sha256":"d57a70d45e4ff3f6f1de7ae93fc143cb955089207637a12f851df358216b1e5e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:04.476260Z","signature_b64":"FnINlCoSAkBX5o3o1SyXyIhZ6foMavgF5ir6IeGnH4Nvx87/h8nGPYZ2zlbeNAopEjpAAQEpXQvXowvHgosGAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bedfd6543134d7c4b266427b904c69b4dde722d4bd4e06eb4aa7f5f94d40ceab","last_reissued_at":"2026-05-18T00:44:04.475494Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:04.475494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On deep holes of generalized projective Reed-Solomon codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.NT","authors_text":"Shaofang Hong, Xiaofan Xu, Yongchao Xu","submitted_at":"2017-05-22T15:59:48Z","abstract_excerpt":"Determining deep holes is an important topic in decoding Reed-Solomon codes. Let $l\\ge 1$ be an integer and $a_1,\\ldots,a_l$ be arbitrarily given $l$ distinct elements of the finite field ${\\bf F}_q$ of $q$ elements with the odd prime number $p$ as its characteristic. Let $D={\\bf F}_q\\backslash\\{a_1,\\ldots,a_l\\}$ and $k$ be an integer such that $2\\le k\\le q-l-1$. In this paper, we study the deep holes of generalized projective Reed-Solomon code ${\\rm GPRS}_q(D, k)$ of length $q-l+1$ and dimension $k$ over ${\\bf F}_q$. 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