{"paper":{"title":"Cyclic bent functions and their applications in codes, codebooks, designs, MUBs and sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chunming Tang, Cunsheng Ding, Maosheng Xiong, Sihem Mesnager","submitted_at":"2018-11-19T14:32:32Z","abstract_excerpt":"Let $m$ be an even positive integer. A Boolean bent function $f$ on $\\GF{m-1} \\times \\GF {}$ is called a \\emph{cyclic bent function} if for any $a\\neq b\\in \\GF {m-1}$ and $\\epsilon \\in \\GF{}$, $f(ax_1,x_2)+f(bx_1,x_2+\\epsilon)$ is always bent, where $x_1\\in \\GF {m-1}, x_2 \\in \\GF {}$. Cyclic bent functions look extremely rare. This paper focuses on cyclic bent functions on $\\GF {m-1} \\times \\GF {}$ and their applications. The first objective of this paper is to construct a new class of cyclic bent functions, which includes all known constructions of cyclic bent functions as special cases. The "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07725","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"}