{"paper":{"title":"New Families of $p$-ary Sequences of Period $\\frac{p^n-1}{2}$ With Low Maximum Correlation Magnitude","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ji-Youp Kim, Jong-Seon No, Wijik Lee","submitted_at":"2013-10-10T02:41:59Z","abstract_excerpt":"Let $p$ be an odd prime such that $p \\equiv 3\\;{\\rm mod}\\;4$ and $n$ be an odd integer. In this paper, two new families of $p$-ary sequences of period $N = \\frac{p^n-1}{2}$ are constructed by two decimated $p$-ary m-sequences $m(2t)$ and $m(dt)$, where $d = 4$ and $d = (p^n + 1)/2=N+1$. The upper bound on the magnitude of correlation values of two sequences in the family is derived using Weil bound. Their upper bound is derived as $\\frac{3}{\\sqrt{2}} \\sqrt{N+\\frac{1}{2}}+\\frac{1}{2}$ and the family size is 4N, which is four times the period of the sequence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2686","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"}