{"paper":{"title":"Computing the generator polynomials of $\\mathbb{Z}_2\\mathbb{Z}_4$-additive cyclic codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Cristina Fern\\'andez-C\\'ordoba, Joaquim Borges Ayats, Roger Ten-Valls","submitted_at":"2016-06-06T13:52:22Z","abstract_excerpt":"A ${\\mathbb{Z}}_2{\\mathbb{Z}}_4$-additive code ${\\cal C}\\subseteq{\\mathbb{Z}}_2^\\alpha\\times{\\mathbb{Z}}_4^\\beta$ is called cyclic if the set of coordinates can be partitioned into two subsets, the set of ${\\mathbb{Z}}_2$ and the set of ${\\mathbb{Z}}_4$ coordinates, such that any simultaneous cyclic shift of the coordinates of both subsets leaves invariant the code. These codes can be identified as submodules of the $\\mathbb{Z}_4[x]$-module $\\mathbb{Z}_2[x]/(x^\\alpha-1)\\times\\mathbb{Z}_4[x]/(x^\\beta-1)$. Any $\\mathbb{Z}_2\\mathbb{Z}_4$-additive cyclic code ${\\cal C}$ is of the form $\\langle (b("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01745","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":""},"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"}