{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:5V2SY6SAXI5LJ5ENOVHFDFBEJR","short_pith_number":"pith:5V2SY6SA","canonical_record":{"source":{"id":"1202.0621","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-02-03T08:13:37Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"93494ebb5d4f6a1fae97ee2b4d9a1b53fc49837b135922cb0d0fc838f924bfd2","abstract_canon_sha256":"cf2fe5ae2a594bc7fc4033c3ee6bc95645c14675f939ad4e34b990b7a03a147c"},"schema_version":"1.0"},"canonical_sha256":"ed752c7a40ba3ab4f48d754e5194244c5d2e5c006ea69b9ea3b4fee50b725f2f","source":{"kind":"arxiv","id":"1202.0621","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0621","created_at":"2026-05-18T03:47:53Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0621v1","created_at":"2026-05-18T03:47:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0621","created_at":"2026-05-18T03:47:53Z"},{"alias_kind":"pith_short_12","alias_value":"5V2SY6SAXI5L","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5V2SY6SAXI5LJ5EN","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5V2SY6SA","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:5V2SY6SAXI5LJ5ENOVHFDFBEJR","target":"record","payload":{"canonical_record":{"source":{"id":"1202.0621","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-02-03T08:13:37Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"93494ebb5d4f6a1fae97ee2b4d9a1b53fc49837b135922cb0d0fc838f924bfd2","abstract_canon_sha256":"cf2fe5ae2a594bc7fc4033c3ee6bc95645c14675f939ad4e34b990b7a03a147c"},"schema_version":"1.0"},"canonical_sha256":"ed752c7a40ba3ab4f48d754e5194244c5d2e5c006ea69b9ea3b4fee50b725f2f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:47:53.174778Z","signature_b64":"bthLDR9iKe3QchOqu+ubCMcAqBTdFIszHbCnO5lOBgY1TpBpQ/xlhqphVw76TNXmQK0N6xRVFnkINoF6tSCvCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed752c7a40ba3ab4f48d754e5194244c5d2e5c006ea69b9ea3b4fee50b725f2f","last_reissued_at":"2026-05-18T03:47:53.174059Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:47:53.174059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.0621","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:47:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ebJXIDUOYgkJPnULH55+wu3TveLi/jJoFr6AbRywqT/quTiPOv/fJrPSUoOJQSOtyFGUN3iiVY5gMDjiWDy9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:32:06.624481Z"},"content_sha256":"a1a026040711fbde42351ea6b5c7e7161720f653a65774319fa6a538911edc0e","schema_version":"1.0","event_id":"sha256:a1a026040711fbde42351ea6b5c7e7161720f653a65774319fa6a538911edc0e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:5V2SY6SAXI5LJ5ENOVHFDFBEJR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New Geometrical Spectra of Linear Codes with Applications to Performance Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"and Qiutao Zhuang, Jia Liu, Xiao Ma","submitted_at":"2012-02-03T08:13:37Z","abstract_excerpt":"In this paper, new enumerating functions for linear codes are defined, including the triangle enumerating function and the tetrahedron enumerating function, both of which can be computed using a trellis-based algorithm over polynomial rings. The computational complexity is dominated by the complexity of the trellis. In addition, we show that these new enumerating functions can be used to improve existing performance bounds on the maximum likelihood decoding."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0621","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:47:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QabxyhcyBy8p6x1IbPjZN2+6mmB7UddMxtENYKC1np3exDcpan8VEvZDbEtugQxzt5sHfBYgM2ZZXbjrRufJCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:32:06.625148Z"},"content_sha256":"551fc65a4719ff30043bf89ed2fd8c62ad57179e956d6bef762bb1384f6e57fa","schema_version":"1.0","event_id":"sha256:551fc65a4719ff30043bf89ed2fd8c62ad57179e956d6bef762bb1384f6e57fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5V2SY6SAXI5LJ5ENOVHFDFBEJR/bundle.json","state_url":"https://pith.science/pith/5V2SY6SAXI5LJ5ENOVHFDFBEJR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5V2SY6SAXI5LJ5ENOVHFDFBEJR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T02:32:06Z","links":{"resolver":"https://pith.science/pith/5V2SY6SAXI5LJ5ENOVHFDFBEJR","bundle":"https://pith.science/pith/5V2SY6SAXI5LJ5ENOVHFDFBEJR/bundle.json","state":"https://pith.science/pith/5V2SY6SAXI5LJ5ENOVHFDFBEJR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5V2SY6SAXI5LJ5ENOVHFDFBEJR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5V2SY6SAXI5LJ5ENOVHFDFBEJR","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":"cf2fe5ae2a594bc7fc4033c3ee6bc95645c14675f939ad4e34b990b7a03a147c","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-02-03T08:13:37Z","title_canon_sha256":"93494ebb5d4f6a1fae97ee2b4d9a1b53fc49837b135922cb0d0fc838f924bfd2"},"schema_version":"1.0","source":{"id":"1202.0621","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0621","created_at":"2026-05-18T03:47:53Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0621v1","created_at":"2026-05-18T03:47:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0621","created_at":"2026-05-18T03:47:53Z"},{"alias_kind":"pith_short_12","alias_value":"5V2SY6SAXI5L","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5V2SY6SAXI5LJ5EN","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5V2SY6SA","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:551fc65a4719ff30043bf89ed2fd8c62ad57179e956d6bef762bb1384f6e57fa","target":"graph","created_at":"2026-05-18T03:47:53Z","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":"In this paper, new enumerating functions for linear codes are defined, including the triangle enumerating function and the tetrahedron enumerating function, both of which can be computed using a trellis-based algorithm over polynomial rings. The computational complexity is dominated by the complexity of the trellis. In addition, we show that these new enumerating functions can be used to improve existing performance bounds on the maximum likelihood decoding.","authors_text":"and Qiutao Zhuang, Jia Liu, Xiao Ma","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-02-03T08:13:37Z","title":"New Geometrical Spectra of Linear Codes with Applications to Performance Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0621","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:a1a026040711fbde42351ea6b5c7e7161720f653a65774319fa6a538911edc0e","target":"record","created_at":"2026-05-18T03:47:53Z","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":"cf2fe5ae2a594bc7fc4033c3ee6bc95645c14675f939ad4e34b990b7a03a147c","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-02-03T08:13:37Z","title_canon_sha256":"93494ebb5d4f6a1fae97ee2b4d9a1b53fc49837b135922cb0d0fc838f924bfd2"},"schema_version":"1.0","source":{"id":"1202.0621","kind":"arxiv","version":1}},"canonical_sha256":"ed752c7a40ba3ab4f48d754e5194244c5d2e5c006ea69b9ea3b4fee50b725f2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed752c7a40ba3ab4f48d754e5194244c5d2e5c006ea69b9ea3b4fee50b725f2f","first_computed_at":"2026-05-18T03:47:53.174059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:47:53.174059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bthLDR9iKe3QchOqu+ubCMcAqBTdFIszHbCnO5lOBgY1TpBpQ/xlhqphVw76TNXmQK0N6xRVFnkINoF6tSCvCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:47:53.174778Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.0621","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1a026040711fbde42351ea6b5c7e7161720f653a65774319fa6a538911edc0e","sha256:551fc65a4719ff30043bf89ed2fd8c62ad57179e956d6bef762bb1384f6e57fa"],"state_sha256":"7fea4d4fb526510fc7a5d4e7e6a8c0dc78489956c837d5c5c6dd39e3c9ca0adb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4SGUnBxHxcZ5cx5R7VLWliqbzAR3eKJQ/SuZPcHQ0AkAT4buOK/7ZOADiYjIzhHP41+2aL5dZAmdI63rkZpLCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T02:32:06.631000Z","bundle_sha256":"48addd5c5436ff12190ecda0ba93f9d424aa3202fc5a853a660896a1b48b97a5"}}