{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:A2MWND2BFVKDNXFNJC52GPGFK2","short_pith_number":"pith:A2MWND2B","canonical_record":{"source":{"id":"1502.04244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-02-14T21:15:43Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"79c6a579956b25b2b184f9f4c7f757b7f115007a87019ea9ae3ccf55cd3e7e9b","abstract_canon_sha256":"023f627dc491c71ed5435bc03ccc663e7adbfeaca96b2c13322345df49ab2433"},"schema_version":"1.0"},"canonical_sha256":"0699668f412d5436dcad48bba33cc55691dfcc7b1eca4b69eaf329e2ca7666e0","source":{"kind":"arxiv","id":"1502.04244","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04244","created_at":"2026-05-18T02:27:00Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04244v1","created_at":"2026-05-18T02:27:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04244","created_at":"2026-05-18T02:27:00Z"},{"alias_kind":"pith_short_12","alias_value":"A2MWND2BFVKD","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"A2MWND2BFVKDNXFN","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"A2MWND2B","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:A2MWND2BFVKDNXFNJC52GPGFK2","target":"record","payload":{"canonical_record":{"source":{"id":"1502.04244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-02-14T21:15:43Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"79c6a579956b25b2b184f9f4c7f757b7f115007a87019ea9ae3ccf55cd3e7e9b","abstract_canon_sha256":"023f627dc491c71ed5435bc03ccc663e7adbfeaca96b2c13322345df49ab2433"},"schema_version":"1.0"},"canonical_sha256":"0699668f412d5436dcad48bba33cc55691dfcc7b1eca4b69eaf329e2ca7666e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:00.151775Z","signature_b64":"KKI0gAAfRg2zU6wviWqwdJR9JzLUajBuhM6JS1OYRIPQZJO60iPkwvvyJLra5fpfVsCv9nOjqA2llL+PIMYMBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0699668f412d5436dcad48bba33cc55691dfcc7b1eca4b69eaf329e2ca7666e0","last_reissued_at":"2026-05-18T02:27:00.151323Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:00.151323Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.04244","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":"2026-05-18T02:27:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LWsicFrqwu2QQC3T7nuP5ks0ubcOfa5+rAcJ0PkyY173qd2NTo26/ynCIkB/FFAFhiif2qYZRgipt02UJVcwCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:14:54.823393Z"},"content_sha256":"5d9793b92a82c135a639077176a901eef527261fb6dc2c3618d3a180aabc239e","schema_version":"1.0","event_id":"sha256:5d9793b92a82c135a639077176a901eef527261fb6dc2c3618d3a180aabc239e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:A2MWND2BFVKDNXFNJC52GPGFK2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal cyclic codes with generalized Niho type zeroes and the weight distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Maosheng Xiong, Nian Li","submitted_at":"2015-02-14T21:15:43Z","abstract_excerpt":"In this paper we extend the works \\cite{gegeng2,XLZD} further in two directions and compute the weight distribution of these cyclic codes under more relaxed conditions. It is interesting to note that many cyclic codes in the family are optimal and have only a few non-zero weights. Besides using similar ideas from \\cite{gegeng2,XLZD}, we carry out some subtle manipulation of certain exponential sums."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04244","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":"2026-05-18T02:27:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KBojF43MAidkpELS6Ur2L2v/WBkw8JQSip8WpwPBaHkQqQzC/SxXpCGuo0MrfHhV16kLE11ZZ3QpuWCpuo3uBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:14:54.823744Z"},"content_sha256":"fb3f28e4bac557f6fceffe22c9b32628f7ef0bed7ece5a91d3edbc430d7b4345","schema_version":"1.0","event_id":"sha256:fb3f28e4bac557f6fceffe22c9b32628f7ef0bed7ece5a91d3edbc430d7b4345"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A2MWND2BFVKDNXFNJC52GPGFK2/bundle.json","state_url":"https://pith.science/pith/A2MWND2BFVKDNXFNJC52GPGFK2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A2MWND2BFVKDNXFNJC52GPGFK2/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":"2026-05-28T01:14:54Z","links":{"resolver":"https://pith.science/pith/A2MWND2BFVKDNXFNJC52GPGFK2","bundle":"https://pith.science/pith/A2MWND2BFVKDNXFNJC52GPGFK2/bundle.json","state":"https://pith.science/pith/A2MWND2BFVKDNXFNJC52GPGFK2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A2MWND2BFVKDNXFNJC52GPGFK2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:A2MWND2BFVKDNXFNJC52GPGFK2","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":"023f627dc491c71ed5435bc03ccc663e7adbfeaca96b2c13322345df49ab2433","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-02-14T21:15:43Z","title_canon_sha256":"79c6a579956b25b2b184f9f4c7f757b7f115007a87019ea9ae3ccf55cd3e7e9b"},"schema_version":"1.0","source":{"id":"1502.04244","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04244","created_at":"2026-05-18T02:27:00Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04244v1","created_at":"2026-05-18T02:27:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04244","created_at":"2026-05-18T02:27:00Z"},{"alias_kind":"pith_short_12","alias_value":"A2MWND2BFVKD","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"A2MWND2BFVKDNXFN","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"A2MWND2B","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:fb3f28e4bac557f6fceffe22c9b32628f7ef0bed7ece5a91d3edbc430d7b4345","target":"graph","created_at":"2026-05-18T02:27:00Z","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 extend the works \\cite{gegeng2,XLZD} further in two directions and compute the weight distribution of these cyclic codes under more relaxed conditions. It is interesting to note that many cyclic codes in the family are optimal and have only a few non-zero weights. Besides using similar ideas from \\cite{gegeng2,XLZD}, we carry out some subtle manipulation of certain exponential sums.","authors_text":"Maosheng Xiong, Nian Li","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-02-14T21:15:43Z","title":"Optimal cyclic codes with generalized Niho type zeroes and the weight distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04244","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":"sha256:5d9793b92a82c135a639077176a901eef527261fb6dc2c3618d3a180aabc239e","target":"record","created_at":"2026-05-18T02:27:00Z","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":"023f627dc491c71ed5435bc03ccc663e7adbfeaca96b2c13322345df49ab2433","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-02-14T21:15:43Z","title_canon_sha256":"79c6a579956b25b2b184f9f4c7f757b7f115007a87019ea9ae3ccf55cd3e7e9b"},"schema_version":"1.0","source":{"id":"1502.04244","kind":"arxiv","version":1}},"canonical_sha256":"0699668f412d5436dcad48bba33cc55691dfcc7b1eca4b69eaf329e2ca7666e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0699668f412d5436dcad48bba33cc55691dfcc7b1eca4b69eaf329e2ca7666e0","first_computed_at":"2026-05-18T02:27:00.151323Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:00.151323Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KKI0gAAfRg2zU6wviWqwdJR9JzLUajBuhM6JS1OYRIPQZJO60iPkwvvyJLra5fpfVsCv9nOjqA2llL+PIMYMBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:00.151775Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.04244","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d9793b92a82c135a639077176a901eef527261fb6dc2c3618d3a180aabc239e","sha256:fb3f28e4bac557f6fceffe22c9b32628f7ef0bed7ece5a91d3edbc430d7b4345"],"state_sha256":"5918247f1be2008d25229ffc95d80112b0b07cb82c4bd66b770b7b39b1f33fe5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KEjwZYJ0+xbwoS0EaNP7d+dWjQ0eoVm0SWXsYRCx3hA8IZ3TWSLrDELYmAExpUjEvdVKSqg6kUR2/einJwazBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T01:14:54.825691Z","bundle_sha256":"41dbfdfdc06b38d9a28bd48c58f0ea0caa2f9e26e769a67b82b5e65bc0970bde"}}