Equivalence classes of matrices over finite fields

Gary L. Mullen

doi:10.1016/0024-3795(79)90031-4

Equivalence classes of matrices over finite fields

Gary L. Mullen

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Let F=GF(q) denote the finite field of order q, and F_mn the ring of m×n matrices over F. Let Ω be a group of permutations of F. If A,B∈F_mn, then A is equivalent to B relative to Ω if there exists ∅∈Ω such that ∅(a_ij) = b_ij. Formulas are given for the number of equivalence classes of a given order and for the total number of classes induced by various permutation groups. In particular, formulas are given if Ω is the symmetric group on q letters, a cyclic group, or a direct sum of cyclic groups.

Original language	English (US)
Pages (from-to)	61-68
Number of pages	8
Journal	Linear Algebra and Its Applications
Volume	27
Issue number	C
DOIs	https://doi.org/10.1016/0024-3795(79)90031-4
State	Published - Oct 1979

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/0024-3795(79)90031-4

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abstract = "Let F=GF(q) denote the finite field of order q, and Fmn the ring of m×n matrices over F. Let Ω be a group of permutations of F. If A,B∈Fmn, then A is equivalent to B relative to Ω if there exists ∅∈Ω such that ∅(aij) = bij. Formulas are given for the number of equivalence classes of a given order and for the total number of classes induced by various permutation groups. In particular, formulas are given if Ω is the symmetric group on q letters, a cyclic group, or a direct sum of cyclic groups.",

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AU - Mullen, Gary L.

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N2 - Let F=GF(q) denote the finite field of order q, and Fmn the ring of m×n matrices over F. Let Ω be a group of permutations of F. If A,B∈Fmn, then A is equivalent to B relative to Ω if there exists ∅∈Ω such that ∅(aij) = bij. Formulas are given for the number of equivalence classes of a given order and for the total number of classes induced by various permutation groups. In particular, formulas are given if Ω is the symmetric group on q letters, a cyclic group, or a direct sum of cyclic groups.

AB - Let F=GF(q) denote the finite field of order q, and Fmn the ring of m×n matrices over F. Let Ω be a group of permutations of F. If A,B∈Fmn, then A is equivalent to B relative to Ω if there exists ∅∈Ω such that ∅(aij) = bij. Formulas are given for the number of equivalence classes of a given order and for the total number of classes induced by various permutation groups. In particular, formulas are given if Ω is the symmetric group on q letters, a cyclic group, or a direct sum of cyclic groups.

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U2 - 10.1016/0024-3795(79)90031-4

DO - 10.1016/0024-3795(79)90031-4

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SP - 61

EP - 68

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - C

ER -

Equivalence classes of matrices over finite fields

Abstract

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