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Title: Nonexistence results on generalized bent functions Zqm→Zq with odd m and q ≡ 2 (mod 4)
Authors: Leung, Ka Hin
Schmidt, Bernhard
Keywords: Science::Mathematics
Issue Date: 2019
Source: Leung, K. H., & Schmidt, B. (2019). Nonexistence results on generalized bent functions Zqm→Zq with odd m and q ≡ 2 (mod 4). Journal of Combinatorial Theory. Series A, 163, 1-33. doi:10.1016/j.jcta.2018.11.007
Journal: Journal of Combinatorial Theory. Series A
Abstract: Let p be an odd prime, let a be a positive integer, let m be an odd positive integer, and suppose that a generalized bent function from Z2pam to Z2pa exists. We show that this implies m≠1, p≤22m+2m+1, and ordp(2)≤2m−1. We obtain further necessary conditions and prove that p=7 if m=3 and p∈{7,23,31,73,89} if m=5. Our results are based on new tools for the investigation of cyclotomic integers of prescribed complex modulus, including “minimal aliases” invariant under automorphisms, and bounds on the ℓ2-norms of their coefficient vectors. These methods have further applications, for instance, to relative difference sets, circulant Butson matrices, and other kinds of bent functions.
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2018.11.007
Rights: © 2018 Elsevier Inc. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
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