{"paper":{"title":"4-Adic Complexity of Interleaved Quaternary Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Keqin Feng, Minghui Yang, Shiyuan Qiang, Xiaoyan Jing","submitted_at":"2021-05-28T13:39:18Z","abstract_excerpt":"Tang and Ding \\cite{X. Tang} present a series of quaternary sequences $w(a, b)$ interleaved by two binary sequences $a$ and $b$ with ideal autocorrelation and show that such interleaved quaternary sequences have optimal autocorrelation. In this paper we consider the 4-adic complexity $FC_{w}(4)$ of such quaternary sequence $w=w(a, b)$. We present a general formula on $FC_{w}(4)$, $w=w(a, b)$. As a direct consequence, we obtain a general lower bound $FC_{w}(4)\\geq\\log_{4}(4^{n}-1)$ where $2n$ is the period of the sequence $w$. By taking $a$ and $b$ to be several types of known binary sequences "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.13826","kind":"arxiv","version":2},"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/2105.13826/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"}