{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6GZZWUQQ4Y5LU4NXLSQLQ25Z2M","short_pith_number":"pith:6GZZWUQQ","canonical_record":{"source":{"id":"1612.00126","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-12-01T03:26:09Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"195284e0f2a8252b605c986c28225267973d6fc2bb763836b3d50a2f091fcc4b","abstract_canon_sha256":"1e28de7a496cc033c550145049464e70205b839fe9a25a76685fdde6d997940f"},"schema_version":"1.0"},"canonical_sha256":"f1b39b5210e63aba71b75ca0b86bb9d305271ee65ac517384a87a659220ca25b","source":{"kind":"arxiv","id":"1612.00126","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.00126","created_at":"2026-05-18T00:53:23Z"},{"alias_kind":"arxiv_version","alias_value":"1612.00126v1","created_at":"2026-05-18T00:53:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.00126","created_at":"2026-05-18T00:53:23Z"},{"alias_kind":"pith_short_12","alias_value":"6GZZWUQQ4Y5L","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6GZZWUQQ4Y5LU4NX","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6GZZWUQQ","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6GZZWUQQ4Y5LU4NXLSQLQ25Z2M","target":"record","payload":{"canonical_record":{"source":{"id":"1612.00126","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-12-01T03:26:09Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"195284e0f2a8252b605c986c28225267973d6fc2bb763836b3d50a2f091fcc4b","abstract_canon_sha256":"1e28de7a496cc033c550145049464e70205b839fe9a25a76685fdde6d997940f"},"schema_version":"1.0"},"canonical_sha256":"f1b39b5210e63aba71b75ca0b86bb9d305271ee65ac517384a87a659220ca25b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:23.995674Z","signature_b64":"Bnx3VswcBeES7z+IHrN7okyDVb65w1Bp6QwWdirBH+GK4A5A6qRfIdUqCnKIQPSNxBWOZTuPiJIxe96lsKMnAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1b39b5210e63aba71b75ca0b86bb9d305271ee65ac517384a87a659220ca25b","last_reissued_at":"2026-05-18T00:53:23.995237Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:23.995237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.00126","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":"2026-05-18T00:53:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8mz1qdRi4PJmX+Vt6CXy/QTuCjIfdjQFXhzeR6wJwDGyrkjcdzW1yYJ0cHAmXn2K4FGGD2N/HnZ5LcLltusgDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T21:53:32.457705Z"},"content_sha256":"3c5eb0b67b5180aa86ddb00bdf4ff15c2debbfa047d2a57f189378f8203ad8d6","schema_version":"1.0","event_id":"sha256:3c5eb0b67b5180aa86ddb00bdf4ff15c2debbfa047d2a57f189378f8203ad8d6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6GZZWUQQ4Y5LU4NXLSQLQ25Z2M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Three-weight codes and the quintic construction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Minjia Shi, Patrick Sol\\'e, Yan Liu","submitted_at":"2016-12-01T03:26:09Z","abstract_excerpt":"We construct a class of three-Lee-weight and two infinite families of five-Lee-weight codes over the ring $R=\\mathbb{F}_2 +v\\mathbb{F}_2 +v^2\\mathbb{F}_2 +v^3\\mathbb{F}_2 +v^4\\mathbb{F}_2,$ where $v^5=1.$ The same ring occurs in the quintic construction of binary quasi-cyclic codes. %The length of these codes depends on the degree $m$ of ring extension. They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using character sums. Given a linear Gray map, we obtain three families of binary abelian codes with few weights. In particular, we obtain a class "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00126","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":"2026-05-18T00:53:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C7SwvAcSYhgz8VAzLUXkszRewnY0R74Hxc13cvJdtAu6MkCNlUuYXwm2DCkXpcpaK7M21GeVD5oknY+wlHTwDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T21:53:32.458264Z"},"content_sha256":"7b44476d2ffed356fa7b229734758c9ef6a31799d2dddbc6627288e1c762f086","schema_version":"1.0","event_id":"sha256:7b44476d2ffed356fa7b229734758c9ef6a31799d2dddbc6627288e1c762f086"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6GZZWUQQ4Y5LU4NXLSQLQ25Z2M/bundle.json","state_url":"https://pith.science/pith/6GZZWUQQ4Y5LU4NXLSQLQ25Z2M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6GZZWUQQ4Y5LU4NXLSQLQ25Z2M/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":"2026-05-18T21:53:32Z","links":{"resolver":"https://pith.science/pith/6GZZWUQQ4Y5LU4NXLSQLQ25Z2M","bundle":"https://pith.science/pith/6GZZWUQQ4Y5LU4NXLSQLQ25Z2M/bundle.json","state":"https://pith.science/pith/6GZZWUQQ4Y5LU4NXLSQLQ25Z2M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6GZZWUQQ4Y5LU4NXLSQLQ25Z2M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6GZZWUQQ4Y5LU4NXLSQLQ25Z2M","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":"1e28de7a496cc033c550145049464e70205b839fe9a25a76685fdde6d997940f","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-12-01T03:26:09Z","title_canon_sha256":"195284e0f2a8252b605c986c28225267973d6fc2bb763836b3d50a2f091fcc4b"},"schema_version":"1.0","source":{"id":"1612.00126","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.00126","created_at":"2026-05-18T00:53:23Z"},{"alias_kind":"arxiv_version","alias_value":"1612.00126v1","created_at":"2026-05-18T00:53:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.00126","created_at":"2026-05-18T00:53:23Z"},{"alias_kind":"pith_short_12","alias_value":"6GZZWUQQ4Y5L","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6GZZWUQQ4Y5LU4NX","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6GZZWUQQ","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:7b44476d2ffed356fa7b229734758c9ef6a31799d2dddbc6627288e1c762f086","target":"graph","created_at":"2026-05-18T00:53:23Z","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":"We construct a class of three-Lee-weight and two infinite families of five-Lee-weight codes over the ring $R=\\mathbb{F}_2 +v\\mathbb{F}_2 +v^2\\mathbb{F}_2 +v^3\\mathbb{F}_2 +v^4\\mathbb{F}_2,$ where $v^5=1.$ The same ring occurs in the quintic construction of binary quasi-cyclic codes. %The length of these codes depends on the degree $m$ of ring extension. They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using character sums. Given a linear Gray map, we obtain three families of binary abelian codes with few weights. In particular, we obtain a class ","authors_text":"Minjia Shi, Patrick Sol\\'e, Yan Liu","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-12-01T03:26:09Z","title":"Three-weight codes and the quintic construction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00126","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":"sha256:3c5eb0b67b5180aa86ddb00bdf4ff15c2debbfa047d2a57f189378f8203ad8d6","target":"record","created_at":"2026-05-18T00:53:23Z","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":"1e28de7a496cc033c550145049464e70205b839fe9a25a76685fdde6d997940f","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-12-01T03:26:09Z","title_canon_sha256":"195284e0f2a8252b605c986c28225267973d6fc2bb763836b3d50a2f091fcc4b"},"schema_version":"1.0","source":{"id":"1612.00126","kind":"arxiv","version":1}},"canonical_sha256":"f1b39b5210e63aba71b75ca0b86bb9d305271ee65ac517384a87a659220ca25b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1b39b5210e63aba71b75ca0b86bb9d305271ee65ac517384a87a659220ca25b","first_computed_at":"2026-05-18T00:53:23.995237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:23.995237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bnx3VswcBeES7z+IHrN7okyDVb65w1Bp6QwWdirBH+GK4A5A6qRfIdUqCnKIQPSNxBWOZTuPiJIxe96lsKMnAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:23.995674Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.00126","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c5eb0b67b5180aa86ddb00bdf4ff15c2debbfa047d2a57f189378f8203ad8d6","sha256:7b44476d2ffed356fa7b229734758c9ef6a31799d2dddbc6627288e1c762f086"],"state_sha256":"4487cf3180a4708d70cf095bfc33fc9bfbcbda8a474eca4642fd33d29b699950"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PMN9LeMDmGPyXaeZ5PufUILho2njLDzQ3XRPO8/iYQDKlhNmxscHZHyeZCT5RXAA8R6i97AhMWx9FMdg85NIAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-18T21:53:32.460349Z","bundle_sha256":"5335a7d1dc820d941ee03ab57f917012a2b45ae78b925ec3461edcbd2e2637bb"}}