{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YNCHTITQZ5KKQPQCLGAV63CZ4Y","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ad804721f77d26354b9ed455be78d15268df7930a0a004addbaae2e691999762","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-29T09:41:36Z","title_canon_sha256":"a847690b2d737b1339708cae57cc5604d447cce54da252c1668911098dab2aaa"},"schema_version":"1.0","source":{"id":"1705.10091","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.10091","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"arxiv_version","alias_value":"1705.10091v1","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10091","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"pith_short_12","alias_value":"YNCHTITQZ5KK","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YNCHTITQZ5KKQPQC","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YNCHTITQ","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:8282008e77ddb2252ae07fd1e37d26b78fc730ce694af7d08ec6481b1b615728","target":"graph","created_at":"2026-05-18T00:43:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"A systematic convolutional encoder of rate $(n-1)/n$ and maximum degree $D$ generates a code of free distance at most ${\\cal D} = D+2$ and, at best, a column distance profile (CDP) of $[2,3,\\ldots,{\\cal D}]$. A code is \\emph{Maximum Distance Separable} (MDS) if it possesses this CDP. Applied on a communication channel over which packets are transmitted sequentially and which loses (erases) packets randomly, such a code allows the recovery from any pattern of $j$ erasures in the first $j$ $n$-packet blocks for $j<{\\cal D}$, with a delay of at most $j$ blocks counting from the first erasure. Thi","authors_text":"\\'Angela Barbero, {\\O}yvind Ytrehus","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-29T09:41:36Z","title":"Rate $(n-1)/n$ Systematic MDS Convolutional Codes over $GF(2^m)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10091","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8a4a3fdbd302d7c552ee6543da6743f5e7f85bf4e1ee96140ed6ed16ab83cd93","target":"record","created_at":"2026-05-18T00:43:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ad804721f77d26354b9ed455be78d15268df7930a0a004addbaae2e691999762","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-29T09:41:36Z","title_canon_sha256":"a847690b2d737b1339708cae57cc5604d447cce54da252c1668911098dab2aaa"},"schema_version":"1.0","source":{"id":"1705.10091","kind":"arxiv","version":1}},"canonical_sha256":"c34479a270cf54a83e0259815f6c59e62ef4fd3468e4cff502e446bb3848cbeb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c34479a270cf54a83e0259815f6c59e62ef4fd3468e4cff502e446bb3848cbeb","first_computed_at":"2026-05-18T00:43:31.977110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:31.977110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Ix6wiaj5eLSQYnT6DpH1dcV4DP1e/A787OxGoSMnt/XGWl9MwZqmk2S/KPhm0aYwyXIdgfK+lF1Fuz7A8GACA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:31.977761Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.10091","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a4a3fdbd302d7c552ee6543da6743f5e7f85bf4e1ee96140ed6ed16ab83cd93","sha256:8282008e77ddb2252ae07fd1e37d26b78fc730ce694af7d08ec6481b1b615728"],"state_sha256":"27b4097e3d469cda1dda2ebec67814361e568176702416c3c66de358cfb07b87"}