## Abstract

We find some necessary conditions for the existence of regular p-ary bent functions (from ℤ_{p}^{n} to ℤ_{p}), where p is a prime. In more detail, we show that there is no regular p-ary bent function f in n variables with w(M_{f}) larger than n/2, and for a given nonnegative integer k, there is no regular p-ary bent function f in n variables with w(M_{f})=n/2-k (n+3/2-k, respectively) for an even n ≥ N _{p,k} (an odd n ≥ N_{p,k}, respectively), where N _{p,k} is some positive integer, which is explicitly determined and the w(M_{f}) of a p-ary function f is some value related to the power of each monomial of f. For the proof of our main results, we use some properties of regular p-ary bent functions, such as the MacWilliams duality, which is proved to hold for regular p-ary bent functions in this paper.

Original language | English |
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Article number | 6725675 |

Pages (from-to) | 1665-1672 |

Number of pages | 8 |

Journal | IEEE Transactions on Information Theory |

Volume | 60 |

Issue number | 3 |

DOIs | |

State | Published - Mar 2014 |

## Keywords

- Gleason theorem
- MacWilliams duality
- p-ary bent function
- p-ary function
- regular p-ary bent function