Homogeneous bent functions of degree n in 2n variables do not exist for n > 3

Tianbing Xia*, Jennifer Seberry, Josef Pieprzyk, Chris Charnes

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)

Abstract

The nonexistance of homogeneous bent functions of degree n in 2n variables for n > 3 was analyzed. For the analysis, a certain decomposition of a Menon difference set, which corrosponds to bent function was used. The results show that there is no homogeneous bent function of degree 4 in 8 Boolean variables. However, it was suggested that there are few execeptions such as 3-homogeneous Boolean functions of 6 variables, and the 2-homogeneous Boolean functions of 4 variables.

Original languageEnglish
Pages (from-to)127-132
Number of pages6
JournalDiscrete Applied Mathematics
Volume142
Issue number1-3 SPEC. ISS.
DOIs
Publication statusPublished - 15 Aug 2004

Keywords

  • Bent
  • Difference sets
  • Homogeneous

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