{"paper":{"title":"On the Hamming Auto- and Cross-correlation Functions of a Class of Frequency Hopping Sequences of Length $ p^{n} $","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CR","authors_text":"Jingling Yuan, Minglong Qi, Shenwu Xiong","submitted_at":"2017-06-14T13:28:02Z","abstract_excerpt":"In this paper, a new class of frequency hopping sequences (FHSs) of length $ p^{n} $ is constructed by using Ding-Helleseth generalized cyclotomic classes of order 2, of which the Hamming auto- and cross-correlation functions are investigated (for the Hamming cross-correlation, only the case $ p\\equiv 3\\pmod 4 $ is considered). It is shown that the set of the constructed FHSs is optimal with respect to the average Hamming correlation functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04479","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"}