{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:2Z7JBGMDIAJZHLVPNRWA5TUSU2","short_pith_number":"pith:2Z7JBGMD","canonical_record":{"source":{"id":"1210.7906","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-10-30T05:51:04Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d58662d65a36d2c74a9209bc5f73f36141a34de3f847dd7e8c8bf163924cf315","abstract_canon_sha256":"4f5b360cd8770723ff4773c76d7a66cfed990ab2e348d741b04aa5c6cf19ec8d"},"schema_version":"1.0"},"canonical_sha256":"d67e909983401393aeaf6c6c0ece92a6a3bb31453da5e2320161a58c9f76947b","source":{"kind":"arxiv","id":"1210.7906","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.7906","created_at":"2026-05-18T03:41:57Z"},{"alias_kind":"arxiv_version","alias_value":"1210.7906v1","created_at":"2026-05-18T03:41:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7906","created_at":"2026-05-18T03:41:57Z"},{"alias_kind":"pith_short_12","alias_value":"2Z7JBGMDIAJZ","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2Z7JBGMDIAJZHLVP","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2Z7JBGMD","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:2Z7JBGMDIAJZHLVPNRWA5TUSU2","target":"record","payload":{"canonical_record":{"source":{"id":"1210.7906","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-10-30T05:51:04Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d58662d65a36d2c74a9209bc5f73f36141a34de3f847dd7e8c8bf163924cf315","abstract_canon_sha256":"4f5b360cd8770723ff4773c76d7a66cfed990ab2e348d741b04aa5c6cf19ec8d"},"schema_version":"1.0"},"canonical_sha256":"d67e909983401393aeaf6c6c0ece92a6a3bb31453da5e2320161a58c9f76947b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:57.716689Z","signature_b64":"DHmYr+6Kp4R0JnHHUAGpCcDVXpCXYfsCpYrs4hmGx4KcalmMHu1/IrOGA7GJRsqiVc8/1ez6S1vLYuLmESlaDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d67e909983401393aeaf6c6c0ece92a6a3bb31453da5e2320161a58c9f76947b","last_reissued_at":"2026-05-18T03:41:57.715847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:57.715847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.7906","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":"2026-05-18T03:41:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kA9/rEoD7lhTKZhT6gYSG3kzT4HqSqqwGYVXHgueNCuNjGbWBhOpobxWqGXRbe0rhK6ODY0AlZ/ICnOXPmp1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:40:15.553408Z"},"content_sha256":"d840dad218ec9d9675fa14e31d5d74c1b7c99f8cf47478008ef4e288550634ee","schema_version":"1.0","event_id":"sha256:d840dad218ec9d9675fa14e31d5d74c1b7c99f8cf47478008ef4e288550634ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:2Z7JBGMDIAJZHLVPNRWA5TUSU2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Synthesis-by-analysis of BCH Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Atta Ul Mustafa, Ghulam Murtaza","submitted_at":"2012-10-30T05:51:04Z","abstract_excerpt":"In this paper we propose a technique to blindly synthesize the generator polynomial of BCH codes. The proposed technique involves finding Greatest Common Divisor (GCD) among different codewords and block lengths. Based on this combinatorial GCD calculation, correlation values are found. For a valid block length, the iterative GCD calculation results either into generator polynomial or some of its higher order multiples. These higher order polynomials are factorized under modulo-2 operation, and one of the resulting factors is always the generator polynomial which further increases the correlat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7906","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":"2026-05-18T03:41:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7czg3Q7I9hp2C1POkVHT4CflKwMBMmJsRCqFAmUr1+FzLKI/YamfOjF++R6EWPxEhO+GszOrVN6/4QX7v0kKAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:40:15.553762Z"},"content_sha256":"b993aa7ff2439f5c001554bcf36a91d623e6905d82f196af00e5dc9c559530a2","schema_version":"1.0","event_id":"sha256:b993aa7ff2439f5c001554bcf36a91d623e6905d82f196af00e5dc9c559530a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2Z7JBGMDIAJZHLVPNRWA5TUSU2/bundle.json","state_url":"https://pith.science/pith/2Z7JBGMDIAJZHLVPNRWA5TUSU2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2Z7JBGMDIAJZHLVPNRWA5TUSU2/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":"2026-06-26T01:40:15Z","links":{"resolver":"https://pith.science/pith/2Z7JBGMDIAJZHLVPNRWA5TUSU2","bundle":"https://pith.science/pith/2Z7JBGMDIAJZHLVPNRWA5TUSU2/bundle.json","state":"https://pith.science/pith/2Z7JBGMDIAJZHLVPNRWA5TUSU2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2Z7JBGMDIAJZHLVPNRWA5TUSU2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2Z7JBGMDIAJZHLVPNRWA5TUSU2","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":"4f5b360cd8770723ff4773c76d7a66cfed990ab2e348d741b04aa5c6cf19ec8d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-10-30T05:51:04Z","title_canon_sha256":"d58662d65a36d2c74a9209bc5f73f36141a34de3f847dd7e8c8bf163924cf315"},"schema_version":"1.0","source":{"id":"1210.7906","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.7906","created_at":"2026-05-18T03:41:57Z"},{"alias_kind":"arxiv_version","alias_value":"1210.7906v1","created_at":"2026-05-18T03:41:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7906","created_at":"2026-05-18T03:41:57Z"},{"alias_kind":"pith_short_12","alias_value":"2Z7JBGMDIAJZ","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2Z7JBGMDIAJZHLVP","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2Z7JBGMD","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:b993aa7ff2439f5c001554bcf36a91d623e6905d82f196af00e5dc9c559530a2","target":"graph","created_at":"2026-05-18T03:41:57Z","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 we propose a technique to blindly synthesize the generator polynomial of BCH codes. The proposed technique involves finding Greatest Common Divisor (GCD) among different codewords and block lengths. Based on this combinatorial GCD calculation, correlation values are found. For a valid block length, the iterative GCD calculation results either into generator polynomial or some of its higher order multiples. These higher order polynomials are factorized under modulo-2 operation, and one of the resulting factors is always the generator polynomial which further increases the correlat","authors_text":"Atta Ul Mustafa, Ghulam Murtaza","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-10-30T05:51:04Z","title":"Synthesis-by-analysis of BCH Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7906","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:d840dad218ec9d9675fa14e31d5d74c1b7c99f8cf47478008ef4e288550634ee","target":"record","created_at":"2026-05-18T03:41:57Z","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":"4f5b360cd8770723ff4773c76d7a66cfed990ab2e348d741b04aa5c6cf19ec8d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-10-30T05:51:04Z","title_canon_sha256":"d58662d65a36d2c74a9209bc5f73f36141a34de3f847dd7e8c8bf163924cf315"},"schema_version":"1.0","source":{"id":"1210.7906","kind":"arxiv","version":1}},"canonical_sha256":"d67e909983401393aeaf6c6c0ece92a6a3bb31453da5e2320161a58c9f76947b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d67e909983401393aeaf6c6c0ece92a6a3bb31453da5e2320161a58c9f76947b","first_computed_at":"2026-05-18T03:41:57.715847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:57.715847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DHmYr+6Kp4R0JnHHUAGpCcDVXpCXYfsCpYrs4hmGx4KcalmMHu1/IrOGA7GJRsqiVc8/1ez6S1vLYuLmESlaDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:57.716689Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.7906","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d840dad218ec9d9675fa14e31d5d74c1b7c99f8cf47478008ef4e288550634ee","sha256:b993aa7ff2439f5c001554bcf36a91d623e6905d82f196af00e5dc9c559530a2"],"state_sha256":"2606c3cc4d682dea83b2823715f6e88129e01c8ca1a57f8ad0fbf16ca7e6147d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iDdM50IHjvJg7DC5UJqOuaqG3qnIJMdWTO1A6E4T5/gFzHBI1GHQo9PxvxcLcYCg0nPzsftzh1l/SzpTR2WIBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T01:40:15.555893Z","bundle_sha256":"f40d5a96d7ef042293b9ee9d44734f8a13646886626707fd077a95f2963a8685"}}