{"paper":{"title":"Non-existence of perfect binary sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"H. Cao, K. Feng, X. Niu","submitted_at":"2018-04-11T04:47:33Z","abstract_excerpt":"Binary sequences with lower autocorrelation values have important applications in cryptography and communications. In this paper, we present all possible parameters for binary periodical sequences with a 2-level autocorrelation values. For $n \\equiv 1\\pmod 4$, we prove some cases of Schmidt's Conjecture for perfect binary sequences. (Des. Codes Cryptogr. 78 (2016), 237-267.) For $n \\equiv 2\\pmod 4$, Jungnickel and Pott (Discrete Appl. Math. 95 (1999) 331-359.) left four perfect binary sequences as open problem and we solve three of its. For $n \\equiv 3\\pmod 4$, we present some nonexistence of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03808","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"}