New nonexistence results on (mn)-generalized bent functions


In this paper, we present some new nonexistence results on (mn)-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 (mn)-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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Correspondence to Qi Wang.

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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.

Communicated by G. Kyureghyan.

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Leung, K.H., Wang, Q. New nonexistence results on (mn)-generalized bent functions. Des. Codes Cryptogr. 88, 755–770 (2020).

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  • Exponent
  • Generalized bent function
  • Minimal relation
  • Nonexistence
  • Vanishing sum

Mathematics Subject Classification

  • 11A07
  • 16S34
  • 05B10
  • 94A15