TY - GEN

T1 - Remarks on Gibbs Permutation Matrices for Ternary Bent Functions

AU - Stanković, Radomir S.

AU - Stanković, Milena

AU - Moraga, Claudio

AU - Astola, Jaakko T.

N1 - Publisher Copyright:
© 2023 IEEE.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - Gibbs permutation matrices

KW - Permutation matrices

KW - Ternary bent functions

KW - Ternary functions

KW - Vilenkin-Chrestenson transform

U2 - 10.1109/ISMVL57333.2023.00024

DO - 10.1109/ISMVL57333.2023.00024

M3 - Conference contribution

AN - SCOPUS:85164610286

T3 - Proceedings of The International Symposium on Multiple-Valued Logic

SP - 70

EP - 75

BT - Proceedings - 2023 IEEE 53rd International Symposium on Multiple-Valued Logic, ISMVL 2023

PB - IEEE

T2 - IEEE International Symposium on Multiple-Valued Logic

Y2 - 22 May 2023 through 24 May 2023

ER -