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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 Thesis (Masters) Zhang, Zhe v, 77, 30 leaves ; 29 cm. Concordia University M.Sc. Mathematics 1997 Francisco, Thaine 264 Concordia University Library 27 Aug 2009 17:10 18 Jan 2018 17:13 http://clues.concordia.ca/search/c?SEARC...
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