Remarks on Gibbs Permutation Matrices for Ternary Bent Functions

Radomir S. Stanković, Milena Stanković, Claudio Moraga, Jaakko T. Astola

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review


As in the binary case, ternary bent functions are a very small portion of the set of all ternary functions for a given number of variables. For example, for n = 2, there are 486 ternary bent functions out of 19683 ternary functions, which is 2, 47%, and this number reduces exponentially with the increase of n. However, finding, or alternatively, constructing them is a challenging task. A possible approach is based upon the manipulation of known ternary bent functions to construct other ternary bent functions. In this paper, we define Gibbs permutation matrices derived from the Gibbs derivative with respect to the Vilenkin-Chrestenson transform and propose their usage in constructing bent functions. The method can be extended to p-valued bent functions, where p is a prime larger than 3.

Original languageEnglish
Title of host publicationProceedings - 2023 IEEE 53rd International Symposium on Multiple-Valued Logic, ISMVL 2023
Number of pages6
ISBN (Electronic)978-1-6654-6416-1
Publication statusPublished - 2023
Publication typeA4 Article in conference proceedings
EventIEEE International Symposium on Multiple-Valued Logic - Matsue, Japan
Duration: 22 May 202324 May 2023

Publication series

NameProceedings of The International Symposium on Multiple-Valued Logic
ISSN (Print)0195-623X
ISSN (Electronic)2378-2226


ConferenceIEEE International Symposium on Multiple-Valued Logic


  • Gibbs permutation matrices
  • Permutation matrices
  • Ternary bent functions
  • Ternary functions
  • Vilenkin-Chrestenson transform

Publication forum classification

  • Publication forum level 1

ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)


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