Equivalence Classes of Matrices Over a Finite Field

Gary L. Mullen

doi:10.1155/S0161171279000387

Equivalence Classes of Matrices Over a Finite Field

Gary L. Mullen

Mathematics

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

2 Scopus citations

Abstract

Let F_q = GF(q) denote the finite field of order q and F(m,q) the ring of mxm matrices over F_q.. Let Ω be a group of permutations of F_q. If A, B ε F(m,q) then A is equivalent to B relative to Ω if there exists φεΩ such that φ(Α) = B where φ(Α) is computed by substitution. Formulas are given for the number of equivalence classes of a given order and for the total number of classes induced by a cyclic group of permutations.

Original language	English (US)
Pages (from-to)	487-491
Number of pages	5
Journal	International Journal of Mathematics and Mathematical Sciences
Volume	2
Issue number	3
DOIs	https://doi.org/10.1155/S0161171279000387
State	Published - 1979

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

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title = "Equivalence Classes of Matrices Over a Finite Field",

abstract = "Let Fq = GF(q) denote the finite field of order q and F(m,q) the ring of mxm matrices over Fq.. Let Ω be a group of permutations of Fq. If A, B ε F(m,q) then A is equivalent to B relative to Ω if there exists φεΩ such that φ(Α) = B where φ(Α) is computed by substitution. Formulas are given for the number of equivalence classes of a given order and for the total number of classes induced by a cyclic group of permutations.",

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AU - Mullen, Gary L.

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N2 - Let Fq = GF(q) denote the finite field of order q and F(m,q) the ring of mxm matrices over Fq.. Let Ω be a group of permutations of Fq. If A, B ε F(m,q) then A is equivalent to B relative to Ω if there exists φεΩ such that φ(Α) = B where φ(Α) is computed by substitution. Formulas are given for the number of equivalence classes of a given order and for the total number of classes induced by a cyclic group of permutations.

AB - Let Fq = GF(q) denote the finite field of order q and F(m,q) the ring of mxm matrices over Fq.. Let Ω be a group of permutations of Fq. If A, B ε F(m,q) then A is equivalent to B relative to Ω if there exists φεΩ such that φ(Α) = B where φ(Α) is computed by substitution. Formulas are given for the number of equivalence classes of a given order and for the total number of classes induced by a cyclic group of permutations.

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JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

IS - 3

ER -

Equivalence Classes of Matrices Over a Finite Field

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