{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GFWEAX7FW5B22BDQSXO5DH3QNQ","short_pith_number":"pith:GFWEAX7F","canonical_record":{"source":{"id":"1704.03311","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-04-11T14:36:46Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"afe0ece18fcc6842e7905bbf4ab6283823076c74d3de5c0d7d234bfaee924e8a","abstract_canon_sha256":"b06704bc4f98f2fa5532494a6660ce026b2af9e5427d5023f8f9c577bc809d84"},"schema_version":"1.0"},"canonical_sha256":"316c405fe5b743ad047095ddd19f706c2bbec72619c4faaebaf077c8f4d13098","source":{"kind":"arxiv","id":"1704.03311","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03311","created_at":"2026-05-18T00:46:32Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03311v1","created_at":"2026-05-18T00:46:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03311","created_at":"2026-05-18T00:46:32Z"},{"alias_kind":"pith_short_12","alias_value":"GFWEAX7FW5B2","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"GFWEAX7FW5B22BDQ","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"GFWEAX7F","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GFWEAX7FW5B22BDQSXO5DH3QNQ","target":"record","payload":{"canonical_record":{"source":{"id":"1704.03311","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-04-11T14:36:46Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"afe0ece18fcc6842e7905bbf4ab6283823076c74d3de5c0d7d234bfaee924e8a","abstract_canon_sha256":"b06704bc4f98f2fa5532494a6660ce026b2af9e5427d5023f8f9c577bc809d84"},"schema_version":"1.0"},"canonical_sha256":"316c405fe5b743ad047095ddd19f706c2bbec72619c4faaebaf077c8f4d13098","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:32.891790Z","signature_b64":"jeJCiTjv+Lyp9lkxbdxSxI7YIzGtreRmNODqRTZ42BzGgaSL0HU1sZ6BdK4UPiKbl4HUaDlBp7NbpTeKRJJ5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"316c405fe5b743ad047095ddd19f706c2bbec72619c4faaebaf077c8f4d13098","last_reissued_at":"2026-05-18T00:46:32.891132Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:32.891132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.03311","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":"2026-05-18T00:46:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6eeTcRX7n2lD5Ca4YeXkYB3BD9cNo46DypyjG0B7mHOxdkACIGsMLIQJqjaz2QIkKNl2pMmY1Hj+AdxFhAWyAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:43:55.987518Z"},"content_sha256":"427fefd358357861639bce5917cbbbc466e93976b6f06025e47f8de4daefa7a3","schema_version":"1.0","event_id":"sha256:427fefd358357861639bce5917cbbbc466e93976b6f06025e47f8de4daefa7a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GFWEAX7FW5B22BDQSXO5DH3QNQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$b$-symbol distance distribution of repeated-root cyclic codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Esra Sengelen Sevim, Hojjat Mostafanasab","submitted_at":"2017-04-11T14:36:46Z","abstract_excerpt":"Symbol-pair codes, introduced by Cassuto and Blaum [1], have been raised for symbol-pair read channels. This new idea is motivated by the limitation of the reading process in high-density data storage technologies. Yaakobi et al. [8] 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 come up with a method to compute the $b$-symbol-pair distance of two $n$-tuples, where $n$ is a positive integer. Also, we deal with the $b$-symbol-pair distances of some kind of cyclic codes of length $p^e$ over $\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03311","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":"2026-05-18T00:46:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f5Hh+Le8F2RUSrw/Ju+dtF5OsL5sFU3eOJU4SLIcHC3XGInNo8y9Z3zxBF+qaACKa0xVHjJGnG5SkyzekcbwBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:43:55.987977Z"},"content_sha256":"135e1c94516fbe76488fe166c94cda13099f489e6ec44c4ce0e44d19a3e26329","schema_version":"1.0","event_id":"sha256:135e1c94516fbe76488fe166c94cda13099f489e6ec44c4ce0e44d19a3e26329"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GFWEAX7FW5B22BDQSXO5DH3QNQ/bundle.json","state_url":"https://pith.science/pith/GFWEAX7FW5B22BDQSXO5DH3QNQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GFWEAX7FW5B22BDQSXO5DH3QNQ/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":"2026-05-31T05:43:55Z","links":{"resolver":"https://pith.science/pith/GFWEAX7FW5B22BDQSXO5DH3QNQ","bundle":"https://pith.science/pith/GFWEAX7FW5B22BDQSXO5DH3QNQ/bundle.json","state":"https://pith.science/pith/GFWEAX7FW5B22BDQSXO5DH3QNQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GFWEAX7FW5B22BDQSXO5DH3QNQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GFWEAX7FW5B22BDQSXO5DH3QNQ","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":"b06704bc4f98f2fa5532494a6660ce026b2af9e5427d5023f8f9c577bc809d84","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-04-11T14:36:46Z","title_canon_sha256":"afe0ece18fcc6842e7905bbf4ab6283823076c74d3de5c0d7d234bfaee924e8a"},"schema_version":"1.0","source":{"id":"1704.03311","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03311","created_at":"2026-05-18T00:46:32Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03311v1","created_at":"2026-05-18T00:46:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03311","created_at":"2026-05-18T00:46:32Z"},{"alias_kind":"pith_short_12","alias_value":"GFWEAX7FW5B2","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"GFWEAX7FW5B22BDQ","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"GFWEAX7F","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:135e1c94516fbe76488fe166c94cda13099f489e6ec44c4ce0e44d19a3e26329","target":"graph","created_at":"2026-05-18T00:46:32Z","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":"Symbol-pair codes, introduced by Cassuto and Blaum [1], have been raised for symbol-pair read channels. This new idea is motivated by the limitation of the reading process in high-density data storage technologies. Yaakobi et al. [8] 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 come up with a method to compute the $b$-symbol-pair distance of two $n$-tuples, where $n$ is a positive integer. Also, we deal with the $b$-symbol-pair distances of some kind of cyclic codes of length $p^e$ over $\\math","authors_text":"Esra Sengelen Sevim, Hojjat Mostafanasab","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-04-11T14:36:46Z","title":"$b$-symbol distance distribution of repeated-root cyclic codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03311","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":"sha256:427fefd358357861639bce5917cbbbc466e93976b6f06025e47f8de4daefa7a3","target":"record","created_at":"2026-05-18T00:46:32Z","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":"b06704bc4f98f2fa5532494a6660ce026b2af9e5427d5023f8f9c577bc809d84","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-04-11T14:36:46Z","title_canon_sha256":"afe0ece18fcc6842e7905bbf4ab6283823076c74d3de5c0d7d234bfaee924e8a"},"schema_version":"1.0","source":{"id":"1704.03311","kind":"arxiv","version":1}},"canonical_sha256":"316c405fe5b743ad047095ddd19f706c2bbec72619c4faaebaf077c8f4d13098","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"316c405fe5b743ad047095ddd19f706c2bbec72619c4faaebaf077c8f4d13098","first_computed_at":"2026-05-18T00:46:32.891132Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:32.891132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jeJCiTjv+Lyp9lkxbdxSxI7YIzGtreRmNODqRTZ42BzGgaSL0HU1sZ6BdK4UPiKbl4HUaDlBp7NbpTeKRJJ5AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:32.891790Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.03311","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:427fefd358357861639bce5917cbbbc466e93976b6f06025e47f8de4daefa7a3","sha256:135e1c94516fbe76488fe166c94cda13099f489e6ec44c4ce0e44d19a3e26329"],"state_sha256":"e9ebe4bebb8a2949c1ce5aeeb0ac5dfadc7a640005ffec8509781ddc480600bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0udyXCOdUIHtNp5VNSaSGkyjzhSLtIN3G7Acs7bz9pYVSyqtwPekEMvkt/TnrRTDdBmX9ZA5HqwW0/2R2GxnCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:43:55.991164Z","bundle_sha256":"654380213951b2cab121cccfe63b694302f90a8d9b81b6ec077b80478d64827f"}}