Equivalence classes of matrices over finite fields

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)61-68
Number of pages8
JournalLinear Algebra and Its Applications
Volume27
Issue numberC
DOIs
StatePublished - Jan 1 1979

Fingerprint

Equivalence classes
Cyclic group
Equivalence class
Galois field
Permutation group
Direct Sum
Symmetric group
Permutation
Denote
Ring
Class

All Science Journal Classification (ASJC) codes

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

Cite this

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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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Equivalence classes of matrices over finite fields. / Mullen, Gary Lee.

In: Linear Algebra and Its Applications, Vol. 27, No. C, 01.01.1979, p. 61-68.

Research output: Contribution to journalArticle

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PY - 1979/1/1

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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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