{"paper":{"title":"MacWilliams type identities on the Lee and Euclidean weights for linear codes over $\\mathbb{Z}_{\\ell}$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Shixin Zhu, Xiaoshan Kai, Yongsheng Tang","submitted_at":"2016-05-29T12:01:44Z","abstract_excerpt":"Motivated by the works of Shiromoto [3] and Shi et al. [4], we study the existence of MacWilliams type identities with respect to Lee and Euclidean weight enumerators for linear codes over $\\mathbb{Z}_{\\ell}.$ Necessary and sufficient conditions for the existence of MacWilliams type identities with respect to Lee and Euclidean weight enumerators for linear codes over $\\mathbb{Z}_{\\ell}$ are given. Some examples about such MacWilliams type identities are also presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08994","kind":"arxiv","version":4},"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"}