{"paper":{"title":"On the Cross-Correlation of a $p$-ary m-Sequence and its Decimated Sequences by $d=\\frac{p^n+1}{p^k+1}+\\frac{p^n-1}{2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.NT"],"primary_cat":"cs.IT","authors_text":"Ji-Youp Kim, Jong-Seon No, Sung-Tai Choi","submitted_at":"2012-05-27T12:36:37Z","abstract_excerpt":"In this paper, for an odd prime $p$ such that $p\\equiv 3\\bmod 4$, odd $n$, and $d=(p^n+1)/(p^k+1)+(p^n-1)/2$ with $k|n$, the value distribution of the exponential sum $S(a,b)$ is calculated as $a$ and $b$ run through $\\mathbb{F}_{p^n}$. The sequence family $\\mathcal{G}$ in which each sequence has the period of $N=p^n-1$ is also constructed. The family size of $\\mathcal{G}$ is $p^n$ and the correlation magnitude is roughly upper bounded by $(p^k+1)\\sqrt{N}/2$. The weight distribution of the relevant cyclic code $\\mathcal{C}$ over $\\mathbb{F}_p$ with the length $N$ and the dimension ${\\rm dim}_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5959","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"}