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Construction of the orthogonal groups of n x n circulant matrices over finite fields

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Construction of the orthogonal groups of n x n circulant matrices over finite fields

Zhang, Zhe (1997) Construction of the orthogonal groups of n x n circulant matrices over finite fields. Masters thesis, Concordia University.

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Abstract

Let F be a finite field with q elements where $q=p\sp{m}, p$ prime. Let ${\cal M}$ be the algebra of n x n circulant matrices over F. The set $O\sb{(n,q)}$ of orthogonal n x n circulant matrices is a subgroup of ${\cal M}\sp\times.$ The major purposes of the thesis are: (1) to explain K. A. Byrd and T. P. Vaughan's results stated in (8), about formulas for the orders, and algorithms for the construction, of the groups $O\sb{(n,q)};$ (2) to show new examples and develop programs to find the orders and to actually construct the group $O\sb{(n,q)}$ for any given n and q.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Zhang, Zhe
Pagination:v, 77, 30 leaves ; 29 cm.
Institution:Concordia University
Degree Name:Theses (M.Sc.)
Program:Mathematics and Statistics
Date:1997
Thesis Supervisor(s):Francisco, Thaine
ID Code:264
Deposited By:Concordia University Libraries
Deposited On:27 Aug 2009 13:10
Last Modified:08 Dec 2010 10:13
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