{"paper":{"title":"Linear complexity problems of level sequences of Euler quotients and their related binary sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR"],"primary_cat":"math.NT","authors_text":"Xiaoni Du, Zhihua Niu, Zhixiong Chen","submitted_at":"2014-09-20T19:02:36Z","abstract_excerpt":"The Euler quotient modulo an odd-prime power $p^r~(r>1)$ can be uniquely decomposed as a $p$-adic number of the form $$ \\frac{u^{(p-1)p^{r-1}} -1}{p^r}\\equiv a_0(u)+a_1(u)p+\\ldots+a_{r-1}(u)p^{r-1} \\pmod {p^r},~ \\gcd(u,p)=1, $$ where $0\\le a_j(u)<p$ for $0\\le j\\le r-1$ and we set all $a_j(u)=0$ if $\\gcd(u,p)>1$. We firstly study certain arithmetic properties of the level sequences $(a_j(u))_{u\\ge 0}$ over $\\mathbb{F}_p$ via introducing a new quotient. Then we determine the exact values of linear complexity of $(a_j(u))_{u\\ge 0}$ and values of $k$-error linear complexity for binary sequences de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2182","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"}