{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4FRQC7EMJSPTOQJGNI3O2TMCUG","short_pith_number":"pith:4FRQC7EM","canonical_record":{"source":{"id":"1609.09236","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-09-29T07:39:31Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"a9b6d4b1c90d9782c0939c9791c04bbddb0ac7799b93fff56030513ea6b2b9c3","abstract_canon_sha256":"db24d3bd1ba86108ad02eebe1cadc5ed8d6166b073d122bea6e597a8d29bd9c4"},"schema_version":"1.0"},"canonical_sha256":"e163017c8c4c9f3741266a36ed4d82a18d107f5d20029e66f495d720c2a4cc8b","source":{"kind":"arxiv","id":"1609.09236","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.09236","created_at":"2026-05-18T01:03:38Z"},{"alias_kind":"arxiv_version","alias_value":"1609.09236v1","created_at":"2026-05-18T01:03:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.09236","created_at":"2026-05-18T01:03:38Z"},{"alias_kind":"pith_short_12","alias_value":"4FRQC7EMJSPT","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4FRQC7EMJSPTOQJG","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4FRQC7EM","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4FRQC7EMJSPTOQJGNI3O2TMCUG","target":"record","payload":{"canonical_record":{"source":{"id":"1609.09236","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-09-29T07:39:31Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"a9b6d4b1c90d9782c0939c9791c04bbddb0ac7799b93fff56030513ea6b2b9c3","abstract_canon_sha256":"db24d3bd1ba86108ad02eebe1cadc5ed8d6166b073d122bea6e597a8d29bd9c4"},"schema_version":"1.0"},"canonical_sha256":"e163017c8c4c9f3741266a36ed4d82a18d107f5d20029e66f495d720c2a4cc8b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:38.411806Z","signature_b64":"SwvVaTtqOs2DgJyM3rHWBbAXeQDankVER39nOEp69e7EZFV1bdIaeUDsWIsovuqOwRcvw1z4ZNTwS+ddSFSkBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e163017c8c4c9f3741266a36ed4d82a18d107f5d20029e66f495d720c2a4cc8b","last_reissued_at":"2026-05-18T01:03:38.411374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:38.411374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.09236","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":"2026-05-18T01:03:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PPv0xckZdfAl3qzamdkltZ1J0dfja2kQpFGP2L1wxg+BcHNUHPQXFOoFKcpib3xbzPfsjSwY5osD2ar9E12DAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:36:41.771162Z"},"content_sha256":"82d792853a2a18728ca92dd8ae81f0d65d8c6c069ca74e02e5d3859ff892cfaa","schema_version":"1.0","event_id":"sha256:82d792853a2a18728ca92dd8ae81f0d65d8c6c069ca74e02e5d3859ff892cfaa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4FRQC7EMJSPTOQJGNI3O2TMCUG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximum Distance Separable Codes for $b$-Symbol Read Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Baokun Ding, Gennian Ge, Tao Zhang","submitted_at":"2016-09-29T07:39:31Z","abstract_excerpt":"Recently, Yaakobi et al. introduced codes for $b$-symbol read channels, where the read operation is performed as a consecutive sequence of $b>2$ symbols. In this paper, we establish a Singleton-type bound on $b$-symbol codes. Codes meeting the Singleton-type bound are called maximum distance separable (MDS) codes, and they are optimal in the sense they attain the maximal minimum $b$-distance. Based on projective geometry and constacyclic codes, we construct new families of linear MDS $b$-symbol codes over finite fields. And in some sense, we completely determine the existence of linear MDS $b$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09236","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":"2026-05-18T01:03:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yiv1Gtsbg3l3ixdnTf08YBY7WEWGO1NNY6BTvQ/anJMYuI1canmpnHqg70Df15KmvnO5S7TI62C4o5PCYSHUDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:36:41.771791Z"},"content_sha256":"66392eaf8bcace2ac37814dbe5eb08445521c493a245340a9210a07f4e3270a3","schema_version":"1.0","event_id":"sha256:66392eaf8bcace2ac37814dbe5eb08445521c493a245340a9210a07f4e3270a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4FRQC7EMJSPTOQJGNI3O2TMCUG/bundle.json","state_url":"https://pith.science/pith/4FRQC7EMJSPTOQJGNI3O2TMCUG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4FRQC7EMJSPTOQJGNI3O2TMCUG/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":"2026-05-27T19:36:41Z","links":{"resolver":"https://pith.science/pith/4FRQC7EMJSPTOQJGNI3O2TMCUG","bundle":"https://pith.science/pith/4FRQC7EMJSPTOQJGNI3O2TMCUG/bundle.json","state":"https://pith.science/pith/4FRQC7EMJSPTOQJGNI3O2TMCUG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4FRQC7EMJSPTOQJGNI3O2TMCUG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4FRQC7EMJSPTOQJGNI3O2TMCUG","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":"db24d3bd1ba86108ad02eebe1cadc5ed8d6166b073d122bea6e597a8d29bd9c4","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-09-29T07:39:31Z","title_canon_sha256":"a9b6d4b1c90d9782c0939c9791c04bbddb0ac7799b93fff56030513ea6b2b9c3"},"schema_version":"1.0","source":{"id":"1609.09236","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.09236","created_at":"2026-05-18T01:03:38Z"},{"alias_kind":"arxiv_version","alias_value":"1609.09236v1","created_at":"2026-05-18T01:03:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.09236","created_at":"2026-05-18T01:03:38Z"},{"alias_kind":"pith_short_12","alias_value":"4FRQC7EMJSPT","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4FRQC7EMJSPTOQJG","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4FRQC7EM","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:66392eaf8bcace2ac37814dbe5eb08445521c493a245340a9210a07f4e3270a3","target":"graph","created_at":"2026-05-18T01:03:38Z","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":"Recently, Yaakobi et al. introduced codes for $b$-symbol read channels, where the read operation is performed as a consecutive sequence of $b>2$ symbols. In this paper, we establish a Singleton-type bound on $b$-symbol codes. Codes meeting the Singleton-type bound are called maximum distance separable (MDS) codes, and they are optimal in the sense they attain the maximal minimum $b$-distance. Based on projective geometry and constacyclic codes, we construct new families of linear MDS $b$-symbol codes over finite fields. And in some sense, we completely determine the existence of linear MDS $b$","authors_text":"Baokun Ding, Gennian Ge, Tao Zhang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-09-29T07:39:31Z","title":"Maximum Distance Separable Codes for $b$-Symbol Read Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09236","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":"sha256:82d792853a2a18728ca92dd8ae81f0d65d8c6c069ca74e02e5d3859ff892cfaa","target":"record","created_at":"2026-05-18T01:03:38Z","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":"db24d3bd1ba86108ad02eebe1cadc5ed8d6166b073d122bea6e597a8d29bd9c4","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-09-29T07:39:31Z","title_canon_sha256":"a9b6d4b1c90d9782c0939c9791c04bbddb0ac7799b93fff56030513ea6b2b9c3"},"schema_version":"1.0","source":{"id":"1609.09236","kind":"arxiv","version":1}},"canonical_sha256":"e163017c8c4c9f3741266a36ed4d82a18d107f5d20029e66f495d720c2a4cc8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e163017c8c4c9f3741266a36ed4d82a18d107f5d20029e66f495d720c2a4cc8b","first_computed_at":"2026-05-18T01:03:38.411374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:38.411374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SwvVaTtqOs2DgJyM3rHWBbAXeQDankVER39nOEp69e7EZFV1bdIaeUDsWIsovuqOwRcvw1z4ZNTwS+ddSFSkBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:38.411806Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.09236","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82d792853a2a18728ca92dd8ae81f0d65d8c6c069ca74e02e5d3859ff892cfaa","sha256:66392eaf8bcace2ac37814dbe5eb08445521c493a245340a9210a07f4e3270a3"],"state_sha256":"815a49499ab8d02655b0da0f6de824cafdfbcb549bc76f6540b0639ccdc2a9c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0c9misRAN/UQO1Pxn0iusqVahGm6MrimTVp6r4uajL7bmHBIdttZrg3kRlZvWbfWGESSsijc+n9nEudHB782Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T19:36:41.774487Z","bundle_sha256":"080841d1ca529c22d636ae49a9897528a71437132a5ebb4ec70fa0e1e2d6813d"}}