Necessary conditions for the existence of regular p-ary bent functions

Jong Yoon Hyun, Heisook Lee, Yoonjin Lee

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We find some necessary conditions for the existence of regular p-ary bent functions (from ℤpn to ℤp), 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(Mf) 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(Mf)=n/2-k (n+3/2-k, respectively) for an even n ≥ N p,k (an odd n ≥ Np,k, respectively), where N p,k is some positive integer, which is explicitly determined and the w(Mf) 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 languageEnglish
Article number6725675
Pages (from-to)1665-1672
Number of pages8
JournalIEEE Transactions on Information Theory
Volume60
Issue number3
DOIs
StatePublished - Mar 2014

Keywords

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

Fingerprint

Dive into the research topics of 'Necessary conditions for the existence of regular p-ary bent functions'. Together they form a unique fingerprint.

Cite this