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This shows that there are infinite families of long QC and QT $t$-CIS codes with relative distance satisfying a modified Varshamov-Gilbert bound for rate $1/t$ codes.\n  Similar results are defined for the new and more gen"},"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":"1703.03109","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-03-09T02:46:24Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"faf03e0a4d40ee996ccdf023f1015da16102ab39b57e041e2650c451fe252ccd","abstract_canon_sha256":"d70c964ebb18b811fc30946d9692aef2ed313d9e963038b10e6287d9bcdc9d30"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:01.513518Z","signature_b64":"L+NVBVjDX/8epVTo2qezyDvFfjn0MjEQXxWiKY+hvKGIOyoiyPsbuhfvMDBRXHLMxEXK3mQpwc+LT1UDlKUyAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5218e2cb78d476cd1131b46eb940cfd3a21fe10ff0feae32c1512d4b67de1bd2","last_reissued_at":"2026-05-18T00:49:01.512808Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:01.512808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Long quasi-polycyclic $t-$CIS codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Adel Alahmadi, Cem G\\\"uneri, Hatoon Shoaib, Patrick Sol\\'e","submitted_at":"2017-03-09T02:46:24Z","abstract_excerpt":"We study complementary information set codes of length $tn$ and dimension $n$ of order $t$ called ($t-$CIS code for short). 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