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

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2018 by IJMTT Journal
Volume-59 Number-4
Year of Publication : 2018
Authors : Briji Jacob Chathely
  10.14445/22315373/IJMTT-V59P532

MLA

MLA Style: Briji Jacob Chathely "Hadamard Matrix and its Application in Coding Theory and Combinatorial Design Theory" International Journal of Mathematics Trends and Technology 59.4 (2018): 218-227.

APA Style: Briji Jacob Chathely (2018). Hadamard Matrix and its Application in Coding Theory and Combinatorial Design Theory. International Journal of Mathematics Trends and Technology, 59(4), 218-227.

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.

Reference
[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

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