Yates Quaternary Complex Hadamard Matrix

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2017 by IJMTT Journal
Volume-50 Number-5
Year of Publication : 2017
Authors : Naseer Ahmad Malik, Hrishikesh Mahato
  10.14445/22315373/IJMTT-V50P548

MLA

Naseer Ahmad Malik, Hrishikesh Mahato "Yates Quaternary Complex Hadamard Matrix", International Journal of Mathematics Trends and Technology (IJMTT). V50(5):298-306 October 2017. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
In this paper we present a construction for a class of 2k X 2k, k ≥ 2 quater- nary complex Hadamard matrix called Yates quaternary complex Hadamard matrix and also we present its properties. It has been observed that every normalized Yates quaternary complex Hadamard matrix of order 2k have full row and column sign spectrum. We also show that Yates quaternary complex Hadamard matrix is a jacket matrix.

Reference
[1] A.S.Hedayat, N.J.A.Sloane and J.Stufken, \Orthogonal Array, Theory and Application" , Springer Verlag, New York (1999).
[2] M.Mitrouli,\D-optimal designs embedded in Hadamard matrices and their effect on the pivot patterns", Linear Algebra Appl., 434 , 1761-1772 (2011).
[3] M. Mitrouli, \A sign test for detecting the equivalence of Sylvester Hadamard matrices" Numer. Algorithms. 57, 169-186 (2011).
[4] J.Seberry and M.Yammada, \Hadamard Matrices ,Sequences and Block Designs, Contemporary Design Theory , A Collection of Surveys", (D.J.Stinson and J.Dinitz, Eds), Jhon Willey and Sons, pp 431-560 (1992).
[5] J.Seberry and M.Mitrouli, \Some remarks on Hadamard matrices", Cryptogra- phy and Communication, 2,293-306 (2010).
[6] K.J.Horadam, \Hadamard Matrices and Their Application", Princeton Univer- sity Press, Princeton and Oxford (2006).
[7] K.J.Horadam and A.Rao, \Fourier Transforms from a Weighted Trace Map", IEEE Xplore (2008).
[8] W.D.Wallis, A.P.Street, J.S.Wallis, \Combinatorics Room Squares, Sum Free Sets ,Hadamard Matrices", "Springer-Verlag Berlin Heidelberg . New York (1972).
[9] Yi Xian Yang, Xin Xin Niu, Cheng Qing Xu, \Theory and Applications of Higher- Dimensional Hadamard Matrices, Second Edition", March 24, by Chapman and Hall/CRC Press (2010).
[10] R.J.Turyn, \Complex Hadamard matrices",Combinatorial Structures and Their Applications, Gordon and Breach, New York,435437 (1970).
[11] W.D.Wallis, A.P.Street and J.S.Wallis, \Combinatorics Room Squares, Sum-Free Sets, Hadamard Matrices", LNM 292 , Springer, Berlin (1972).
[12] J.J.Sylvester, \Thoughts on inverse orthogonal matrices, simultaneous sign successions, and tesselated pavements in two or more colours, with applications to Newton's rule, ornamental tile work,and the theory of numbers", Phil. Mag. (4) 34,461-475 (1867).
[13] D.C.Montgomery, \Design and Analysis of Experiments,",6th edn. Wiley, New York (2005).
[14] F.Yates, \Design and Analysis of Factorial Experiments,",Tech. Comm. No. 35, Imperial Bureau of Soil Sciences, London, (1937).

Keywords
Yates Quaternary Complex Hadamard Matrix, Complex Sign Changes, Sign Spectrum, Jacket Matrix.