A NOTE OF EQUIVALENCE CLASSES OF MATRICES OVERA FINITE FIELD

Let Fqm×m denote the algebra of m×m matrices over the finite field Fq of q elements, and let Ω denote a group of permutations of Fq. It is well known that each ϕϵΩ can be represented uniquely by a polynomial ϕ(x)ϵFq[x] of degree less than q; thus, the group Ω naturally determines a relation ∼ on Fqm×m as follows: if A,BϵFqm×m then A∼B if ϕ(A)=B for some ϕϵΩ. Here ϕ(A) is to be interpreted as substitution into the unique polynomial of degree

Keywords:

• Mathematics
• Permutation
• Mathematical analysis
• Combinatorics
• Equivalence class
• Finite field
• Algebra
• Polynomial
• Matrix (mathematics)
• Discrete mathematics

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