{"paper":{"title":"Structure of Cayley Codes","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Cheryl E. Praeger, Daniel Rademacher, Vishnuram Arumugam","submitted_at":"2026-06-26T21:11:11Z","abstract_excerpt":"Cayley codes, introduced by Kaufman and Wigderson, are linear codes constructed from a Cayley graph and a smaller linear code. We explore general properties of the class of Cayley codes for finite groups. In particular we give a reduction to Cayley codes for connected Cayley graphs that maintains code properties such as rate, minimum distance and symmetry. Also, for a given Cayley code, we identify a family of symmetric Cayley codes, each associated with a normal edge-transitive Cayley graph, such that the given Cayley code embeds into the direct sum of the symmetric Cayley codes. We analyse s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28611","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.28611/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}