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 -