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2011•Unpublished venueRequires access

HADAMARD MATRICES AND THEIR DESIGNS

Omar Abdulrahman Al-Attas

Open publisher page 1 citations

Abstract

The main aim of this thesis is to give a survey of Hadamard matrices and their designs. We studied the construction of Hadamard matrices and the relation between Hadamard matrices and their designs. Also, we conclude Theorem (2.2.16) in which given the existence property of Hadamard matrices which is Let be a positive integer, and Then 1. If is prime power for some , then there exists a Hadamard matrix of order n. 2. If there is such that is prime power, and there is , such that is prime power, then there exists a Hadamard matrix of order n. Finally, we studied Regular Hadamard matrices and their relationship with Menon design.

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What this paper is about

The main aim of this thesis is to give a survey of Hadamard matrices and their designs. We studied the construction of Hadamard matrices and the relation between Hadamard matrices and their designs. Also, we conclude Theorem (2.2.16) in which given the existence property of Hadamard matrices which is Let be a positive integer, and Then 1. If is prime power for some , then there exists a Hadamard matrix of order n. 2. If there is such that is prime power, and there is , such that is prime power, then there exists a Hadamard matrix of order n. Finally, we studied Regular Hadamard matrices and their relationship with Menon design.

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Available abstract

The main aim of this thesis is to give a survey of Hadamard matrices and their designs. We studied the construction of Hadamard matrices and the relation between Hadamard matrices and their designs. Also, we conclude Theorem (2.2.16) in which given the existence property of Hadamard matrices which is Let be a positive integer, and Then 1. If is prime power for some , then there exists a Hadamard matrix of order n. 2. If there is such that is prime power, and there is , such that is prime power, then there exists a Hadamard matrix of order n. Finally, we studied Regular Hadamard matrices and their relationship with Menon design.

Key concepts: Hadamard transform, Hadamard matrix, Hadamard's inequality, Mathematics, Hadamard's maximal determinant problem, Complex Hadamard matrix, Prime power, Hadamard three-lines theorem

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