Abstract
In this paper, we present some new nonexistence results on (m, n)-generalized bent functions, which improved recent results. More precisely, we derive new nonexistence results for general n and m odd or \(m \equiv 2 \pmod {4}\), and further explicitly prove nonexistence of (m, 3)-generalized bent functions for all integers m odd or \(m \equiv 2 \pmod {4}\). The main tools we utilized are certain exponents of minimal vanishing sums from applying characters to group ring equations that characterize (m, n)-generalized bent functions.
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The authors are very grateful to the two anonymous reviewers for all their detailed comments that improved the quality and the presentation of this paper.
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Communicated by G. Kyureghyan.
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K.H. Leung’s research was supported by Grant R-146-000-158-112, Ministry of Education, Singapore. Q. Wang’s research was supported by the National Natural Science Foundation of China under Grant 61672015.
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Leung, K.H., Wang, Q. New nonexistence results on (m, n)-generalized bent functions. Des. Codes Cryptogr. 88, 755–770 (2020). https://doi.org/10.1007/s10623-019-00708-8
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DOI: https://doi.org/10.1007/s10623-019-00708-8