{"paper":{"title":"On the distinctness of binary sequences derived from $2$-adic expansion of m-sequences over finite prime fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Dongdai Lin, Yupeng Jiang","submitted_at":"2014-02-19T08:42:52Z","abstract_excerpt":"Let $p$ be an odd prime with $2$-adic expansion $\\sum_{i=0}^kp_i\\cdot2^i$. For a sequence $\\underline{a}=(a(t))_{t\\ge 0}$ over $\\mathbb{F}_{p}$, each $a(t)$ belongs to $\\{0,1,\\ldots, p-1\\}$ and has a unique $2$-adic expansion $$a(t)=a_0(t)+a_1(t)\\cdot 2+\\cdots+a_{k}(t)\\cdot2^k,$$ with $a_i(t)\\in\\{0, 1\\}$. Let $\\underline{a_i}$ denote the binary sequence $(a_i(t))_{t\\ge 0}$ for $0\\le i\\le k$. Assume $i_0$ is the smallest index $i$ such that $p_{i}=0$ and $\\underline{a}$ and $\\underline{b}$ are two different m-sequences generated by a same primitive characteristic polynomial over $\\mathbb{F}_p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4590","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"}