{"paper":{"title":"A Construction of Linear Codes and Their Complete Weight Enumerators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chunming Tang, Shudi Yang, Xiangli Kong","submitted_at":"2017-01-09T06:55:52Z","abstract_excerpt":"Recently, linear codes constructed from defining sets have been studied extensively. They may have nice parameters if the defining set is chosen properly. Let $ m >2$ be a positive integer. For an odd prime $ p $, let $ r=p^m $ and $\\text{Tr}$ be the absolute trace function from $\\mathbb{F}_r$ onto $\\mathbb{F}_p$. In this paper, we give a construction of linear codes by defining the code $ C_{D}=\\{(\\mathrm{Tr}(ax))_{x\\in D}: a \\in \\mathbb{F}_{r} \\}, $ where $ D =\\left\\{x\\in \\mathbb{F}_{r} : \\mathrm{Tr}(x)=1, \\mathrm{Tr}(x^2)=0 \\right\\}. $ Its complete weight enumerator and weight enumerator ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02075","kind":"arxiv","version":3},"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"}