{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:BVCNTUSD7FUJR7AEPFPF4RMPY7","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":"fbaebdf58e6fed3981794dd681986197c39ac443cf3f5140b15b17b06298b85a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-09-20T08:14:56Z","title_canon_sha256":"104175249e3f83a8a03f1e9942f63c9f0821fb49d5d87c67576c8e2779e69e31"},"schema_version":"1.0","source":{"id":"1009.3728","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.3728","created_at":"2026-05-18T03:19:12Z"},{"alias_kind":"arxiv_version","alias_value":"1009.3728v2","created_at":"2026-05-18T03:19:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3728","created_at":"2026-05-18T03:19:12Z"},{"alias_kind":"pith_short_12","alias_value":"BVCNTUSD7FUJ","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BVCNTUSD7FUJR7AE","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BVCNTUSD","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:8e43ad5adbff4447249085e9f98337117bd846e25aba2afaa019f3f43c473336","target":"graph","created_at":"2026-05-18T03:19:12Z","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":"Existing construction algorithms of block network-error correcting codes require a rather large field size, which grows with the size of the network and the number of sinks, and thereby can be prohibitive in large networks. In this work, we give an algorithm which, starting from a given network-error correcting code, can obtain another network code using a small field, with the same error correcting capability as the original code. An algorithm for designing network codes using small field sizes proposed recently by Ebrahimi and Fragouli can be seen as a special case of our algorithm. The majo","authors_text":"B. Sundar Rajan, K. Prasad","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-09-20T08:14:56Z","title":"Network-Error Correcting Codes using Small Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3728","kind":"arxiv","version":2},"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":"sha256:1eb9ce975eba2dde9737b16c38d0074d326eccd9bf7f6b88ac47e8a052e7d8ed","target":"record","created_at":"2026-05-18T03:19:12Z","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":"fbaebdf58e6fed3981794dd681986197c39ac443cf3f5140b15b17b06298b85a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-09-20T08:14:56Z","title_canon_sha256":"104175249e3f83a8a03f1e9942f63c9f0821fb49d5d87c67576c8e2779e69e31"},"schema_version":"1.0","source":{"id":"1009.3728","kind":"arxiv","version":2}},"canonical_sha256":"0d44d9d243f96898fc04795e5e458fc7e45aa823f01da90b484822e422a29c87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d44d9d243f96898fc04795e5e458fc7e45aa823f01da90b484822e422a29c87","first_computed_at":"2026-05-18T03:19:12.024072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:12.024072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+MPselIiTeOu81ojXgQP2Kv5HJFIXlvry+csSnm2FNdNkD5qB+mH88bGCkBC42OOGBse8abYAvjufQfYoQHmAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:12.024527Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.3728","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1eb9ce975eba2dde9737b16c38d0074d326eccd9bf7f6b88ac47e8a052e7d8ed","sha256:8e43ad5adbff4447249085e9f98337117bd846e25aba2afaa019f3f43c473336"],"state_sha256":"923ea056ff91604cd587916ec1fb487f3939a70ab3e05f8a1123ba8ebd1dd462"}