Hadamard Matrix and its Application in Coding Theory and Combinatorial Design Theory

Briji Jacob Chathely

doi:https://doi.org/10.14445/22315373/IJMTT-V59P532

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 59 | Number 4 | Year 2018 | Article Id. IJMTT-V59P532 | DOI : https://doi.org/10.14445/22315373/IJMTT-V59P532

Hadamard Matrix and its Application in Coding Theory and Combinatorial Design Theory

Briji Jacob Chathely

Citation :

Briji Jacob Chathely, "Hadamard Matrix and its Application in Coding Theory and Combinatorial Design Theory," International Journal of Mathematics Trends and Technology (IJMTT), vol. 59, no. 4, pp. 218-227, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V59P532

Abstract

Matrix theory is widely used in a variety of areas including applied mathematics, computer science, economics, engineering, operations research, statistics and others. This paper presents the study of Hadamard Matrices. There are theorems and properties related to this matrix. Also the construction of Hadamard codes and Hadamard 2- Design using Hadamard matrices is discussed in this paper.

Keywords

orthogonal, eigenvalues, tensor product, linear codes, codeword, hamming distance.

References

[1] S. Kumaresan. Linear Algebra: A Geometric Approach. Prentice-Hall of India Pvt.Ltd, India.
[2] Fuzhen Zhang. Matrix Theory Basic Results and Techniques. USA:Springer International Edition,1999.
[3] F. J. MacWilliams, N. J. A. Sloane. The Theory of Error- Correcting Codes. North Holland Publishing Company, New York.
[4] K. J. Horadam. Hadamard Matrices and their Applications. Princeton University Press, Princeton.
[5] Ian Anderson; Iiro Honkala. A Short Course in Combinatorial Designs. Internet Edition, Spring 1997, Revised 2012.
[6] Hadamard Matrices, http://www.sfu.ca/mdevos/notes/comb struct/hadamard.pdf
[7] Hadamard Matrices, http://people.cs.uchicago.edu/laci/reu02
[8] Hadamard Codes, http://www.mcs.csueastbay.edu/malek/TeX/Hadamard.pdf
[9] Linear Codes, http://www.math.ualberta.ca/hongchen/m422/Chap3.pdf