Academic Journal of Mathematical Sciences, 2024, 5(1); doi: 10.25236/AJMS.2024.050113.
Yuying Ou, Wenbin Zhang
Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou, China
In this paper, we consider the matrix representations of the finite field, and show some conclusions of the primitive matrix representation of the finite field on the ground field by using the properties of the cyclotomic polynomial. We obtain the symmetric matrix representation of the finite field Fq with characteristic 2 by constructing the symmetric matrix, and get the relationship between the symmetric matrix representation and the primitive matrix representation of the finite field Fq.
Finite field; Primitive matrix representation; Cyclotomic polynomial; Primitive polynomial; Symmetric matrix representation
Yuying Ou, Wenbin Zhang. The Primitive Matrix Representation and Symmetric Matrix Representation of Finite Fields. Academic Journal of Mathematical Sciences (2024) Vol. 5, Issue 1: 89-95. https://doi.org/10.25236/AJMS.2024.050113.
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