Fastest classes of linearly independent transforms over GF(3) and their properties

New Fastest Linearly Independent Transforms over GF(3)

“…Extension of the known ternary fastest LI transforms [6] to generate new classes of ternary fastest LI transforms with the same lowest computational cost have been presented. Several properties and relations for the transforms have also been given.…”

“…From Definition 9 and the relations between the ternary fastest LI transform matrices of classes Y1 and Z1 presented in [6], it can be established that Let the matrix Z be defined as …”

“…Groups of ternary LI transforms with lower computational cost than ternary Reed-Muller transform have been presented in [6] where they are classified into classes Y1, Y2, Z1, and Z2 based on their structure. There are six ternary LI transforms inside each class, where four of them have the same computational costs that are lower than the computational cost of the other two transforms in the class.…”

“…All the known ternary fastest LI transforms presented in [6] are recursive and can be defined in terms of the submatrices R on a n n 3 3 × matrix n M is defined as recursively applying operator…”

“…In this paper, new fastest LI transforms over GF (3) and their properties are investigated and compared with the known fastest LI transforms over GF(3) [6]. The presented transforms and their properties shown here can be used as bases for analysis, synthesis, and testing of ternary functions as well as creating their spectral decision diagrams in a similar manner as for other polynomial expansions [1,7,8].…”