{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:5HZMMGRLEI6IH7RYMQX7J3V3UQ","short_pith_number":"pith:5HZMMGRL","schema_version":"1.0","canonical_sha256":"e9f2c61a2b223c83fe38642ff4eebba424756228b5662f63fc6d8256e2514d25","source":{"kind":"arxiv","id":"1506.03792","version":2},"attestation_state":"computed","paper":{"title":"Convolutional Codes with Maximum Column Sum Rank for Network Streaming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ahmed Badr, Ashish Khisti, Rafid Mahmood","submitted_at":"2015-06-11T19:32:27Z","abstract_excerpt":"The column Hamming distance of a convolutional code determines the error correction capability when streaming over a class of packet erasure channels. We introduce a metric known as the column sum rank, that parallels column Hamming distance when streaming over a network with link failures. We prove rank analogues of several known column Hamming distance properties and introduce a new family of convolutional codes that maximize the column sum rank up to the code memory. Our construction involves finding a class of super-regular matrices that preserve this property after multiplication with non"},"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":"1506.03792","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-11T19:32:27Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9efb6676f0378dfeb4200426c8709b85083754252895dd252adcbc90f5a2d95d","abstract_canon_sha256":"9c30cfb5a581a219efa50cb0bd3093c0d548e3f56caf2b370224d5f07f8851c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:00.711965Z","signature_b64":"P2oogID+7H6AfeiuwUviyCEVSNpLNOkb1g34g0tfxyajNKLttK7nzHijIwLUVbSL1NQPzx3nooZwafMm0GcGDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9f2c61a2b223c83fe38642ff4eebba424756228b5662f63fc6d8256e2514d25","last_reissued_at":"2026-05-18T01:17:00.711298Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:00.711298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convolutional Codes with Maximum Column Sum Rank for Network Streaming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ahmed Badr, Ashish Khisti, Rafid Mahmood","submitted_at":"2015-06-11T19:32:27Z","abstract_excerpt":"The column Hamming distance of a convolutional code determines the error correction capability when streaming over a class of packet erasure channels. We introduce a metric known as the column sum rank, that parallels column Hamming distance when streaming over a network with link failures. We prove rank analogues of several known column Hamming distance properties and introduce a new family of convolutional codes that maximize the column sum rank up to the code memory. Our construction involves finding a class of super-regular matrices that preserve this property after multiplication with non"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03792","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1506.03792","created_at":"2026-05-18T01:17:00.711416+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.03792v2","created_at":"2026-05-18T01:17:00.711416+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03792","created_at":"2026-05-18T01:17:00.711416+00:00"},{"alias_kind":"pith_short_12","alias_value":"5HZMMGRLEI6I","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"5HZMMGRLEI6IH7RY","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"5HZMMGRL","created_at":"2026-05-18T12:29:05.191682+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5HZMMGRLEI6IH7RYMQX7J3V3UQ","json":"https://pith.science/pith/5HZMMGRLEI6IH7RYMQX7J3V3UQ.json","graph_json":"https://pith.science/api/pith-number/5HZMMGRLEI6IH7RYMQX7J3V3UQ/graph.json","events_json":"https://pith.science/api/pith-number/5HZMMGRLEI6IH7RYMQX7J3V3UQ/events.json","paper":"https://pith.science/paper/5HZMMGRL"},"agent_actions":{"view_html":"https://pith.science/pith/5HZMMGRLEI6IH7RYMQX7J3V3UQ","download_json":"https://pith.science/pith/5HZMMGRLEI6IH7RYMQX7J3V3UQ.json","view_paper":"https://pith.science/paper/5HZMMGRL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.03792&json=true","fetch_graph":"https://pith.science/api/pith-number/5HZMMGRLEI6IH7RYMQX7J3V3UQ/graph.json","fetch_events":"https://pith.science/api/pith-number/5HZMMGRLEI6IH7RYMQX7J3V3UQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5HZMMGRLEI6IH7RYMQX7J3V3UQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5HZMMGRLEI6IH7RYMQX7J3V3UQ/action/storage_attestation","attest_author":"https://pith.science/pith/5HZMMGRLEI6IH7RYMQX7J3V3UQ/action/author_attestation","sign_citation":"https://pith.science/pith/5HZMMGRLEI6IH7RYMQX7J3V3UQ/action/citation_signature","submit_replication":"https://pith.science/pith/5HZMMGRLEI6IH7RYMQX7J3V3UQ/action/replication_record"}},"created_at":"2026-05-18T01:17:00.711416+00:00","updated_at":"2026-05-18T01:17:00.711416+00:00"}