A note of equivalence classes of matrices over a 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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1981-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171281000161 |
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| Summary: | 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 <q which represents ϕ. |
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| ISSN: | 0161-1712 1687-0425 |