{"paper":{"title":"Self-orthogonal generalized twisted Reed-Solomon codes","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Canze Zhu, Qunying Liao","submitted_at":"2022-01-08T04:12:46Z","abstract_excerpt":"In this paper, by calculating the dual code of the Schur square for the standard twisted Reed-Solomon code, we give a sufficient and necessary condition for the generalized twisted Reed-Solomon code with $h+t\\le k-1$ to be self-orthogonal, where $k$ is dimension, $h$ is hook and $t$ is twist. And then, we show that there is no self-orthogonal generalized twisted Reed-Solomon code under some conditions. Furthermore, several classes of self-orthogonal generalized twisted Reed-Solomon codes are constructed, and some of these codes are non-GRS self-orthogonal MDS codes or NMDS codes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.02758","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/2201.02758/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"}