{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:6HHPUWOII5CIFDZHJNW3IM4AYL","short_pith_number":"pith:6HHPUWOI","schema_version":"1.0","canonical_sha256":"f1cefa59c84744828f274b6db43380c2d7cd2beb223a43e8fa388f189dc474fa","source":{"kind":"arxiv","id":"1109.4770","version":2},"attestation_state":"computed","paper":{"title":"On the algebraic representation of selected optimal non-linear binary codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Jens Zumbr\\\"agel, Marcus Greferath","submitted_at":"2011-09-22T11:03:51Z","abstract_excerpt":"Revisiting an approach by Conway and Sloane we investigate a collection of optimal non-linear binary codes and represent them as (non-linear) codes over Z4. The Fourier transform will be used in order to analyze these codes, which leads to a new algebraic representation involving subgroups of the group of units in a certain ring.\n  One of our results is a new representation of Best's (10, 40, 4) code as a coset of a subgroup in the group of invertible elements of the group ring Z4[Z5]. This yields a particularly simple algebraic decoding algorithm for this code.\n  The technique at hand is furt"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1109.4770","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-22T11:03:51Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"d6b01256f5a46ceb82c81d379f08176665ebdbb6e551ba9355c58935085e0a65","abstract_canon_sha256":"4913b5b2eb0d2a5ff5fea97460b1044025decac2f568ac6ca022c12ca31e66f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:06.702651Z","signature_b64":"D7/BUeeB7tVfi9/ZfIjicZw67SkJErpyKdebrgAkEP8PRdM9XlPE7vc9CrQuesTOTW9pUJri30se5e6906q/Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1cefa59c84744828f274b6db43380c2d7cd2beb223a43e8fa388f189dc474fa","last_reissued_at":"2026-05-18T04:03:06.701862Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:06.701862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the algebraic representation of selected optimal non-linear binary codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Jens Zumbr\\\"agel, Marcus Greferath","submitted_at":"2011-09-22T11:03:51Z","abstract_excerpt":"Revisiting an approach by Conway and Sloane we investigate a collection of optimal non-linear binary codes and represent them as (non-linear) codes over Z4. The Fourier transform will be used in order to analyze these codes, which leads to a new algebraic representation involving subgroups of the group of units in a certain ring.\n  One of our results is a new representation of Best's (10, 40, 4) code as a coset of a subgroup in the group of invertible elements of the group ring Z4[Z5]. This yields a particularly simple algebraic decoding algorithm for this code.\n  The technique at hand is furt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4770","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1109.4770","created_at":"2026-05-18T04:03:06.701988+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.4770v2","created_at":"2026-05-18T04:03:06.701988+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4770","created_at":"2026-05-18T04:03:06.701988+00:00"},{"alias_kind":"pith_short_12","alias_value":"6HHPUWOII5CI","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"6HHPUWOII5CIFDZH","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"6HHPUWOI","created_at":"2026-05-18T12:26:22.705136+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6HHPUWOII5CIFDZHJNW3IM4AYL","json":"https://pith.science/pith/6HHPUWOII5CIFDZHJNW3IM4AYL.json","graph_json":"https://pith.science/api/pith-number/6HHPUWOII5CIFDZHJNW3IM4AYL/graph.json","events_json":"https://pith.science/api/pith-number/6HHPUWOII5CIFDZHJNW3IM4AYL/events.json","paper":"https://pith.science/paper/6HHPUWOI"},"agent_actions":{"view_html":"https://pith.science/pith/6HHPUWOII5CIFDZHJNW3IM4AYL","download_json":"https://pith.science/pith/6HHPUWOII5CIFDZHJNW3IM4AYL.json","view_paper":"https://pith.science/paper/6HHPUWOI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.4770&json=true","fetch_graph":"https://pith.science/api/pith-number/6HHPUWOII5CIFDZHJNW3IM4AYL/graph.json","fetch_events":"https://pith.science/api/pith-number/6HHPUWOII5CIFDZHJNW3IM4AYL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6HHPUWOII5CIFDZHJNW3IM4AYL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6HHPUWOII5CIFDZHJNW3IM4AYL/action/storage_attestation","attest_author":"https://pith.science/pith/6HHPUWOII5CIFDZHJNW3IM4AYL/action/author_attestation","sign_citation":"https://pith.science/pith/6HHPUWOII5CIFDZHJNW3IM4AYL/action/citation_signature","submit_replication":"https://pith.science/pith/6HHPUWOII5CIFDZHJNW3IM4AYL/action/replication_record"}},"created_at":"2026-05-18T04:03:06.701988+00:00","updated_at":"2026-05-18T04:03:06.701988+00:00"}