Some Infinite Series of Weighing Matrices From Hadamard Matrices

Gopal Prajapati; Mithilesh Kumar Singh

doi:https://doi.org/10.14445/22315373/IJMTT-V54P523

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 54 | Number 3 | Year 2018 | Article Id. IJMTT-V54P523 | DOI : https://doi.org/10.14445/22315373/IJMTT-V54P523

Some Infinite Series of Weighing Matrices From Hadamard Matrices

Gopal Prajapati, Mithilesh Kumar Singh

Abstract

In this paper we have constructed four infinite series of weighing matrices from Hadamard matrices with the help of compound matrices.

Keywords

Hadamard matrix, r-Compound matrix, Weighing matrix.

References

[1] K.T. Arasu, K.H. Leung, S.L. ma, A.Nabavi, D.K , Ray Chaudhury, Circulant weighing matrices of weight 22t ,Springer Journals Vol. 41(2006)111-123.
[2] G. Berman, Families of generalized weighing matrices, Canadian J. Math.30, p 14-28 (1978).
[3] H.J. Briegel, and R. Raussendorf, Persistent entanglement in arrays of interacting particles, Phys.Rev. Lett. 86 910(2001)
[4] S.T. Flammia, ,and S. Severini, Weighing matrices and optical quantum computing , J. Phys. A:Math.Theor 42(2009)065302
[5] Anthony V. Geramita, Norman J. Pullman, and Jennifer S. Wallis, Families of Weighing matrices, Bull. Austral. Math. Soc. Vol.-10(1974) 119-122.
[6] Marc Gysin and J.Sebberry, The weighing matrices of order 4n and weight 4n-2 and 2n-1 , Australasian Journal of Combinatorics, Vol. 12 (1995), 157-174.
[7] Marc Gysin and J.Sebberry, New Weighing matrices through Linear Combinations of generalized cosets, In Conference on combinatorial Mathematics and Combinatorian, University of Technology,Sydney,july 1996.
[8] M. Hall Jr., Combinatorial theory, Wiley ,New York p.238 (1998).
[9] R. A. Horn, and C. R. Johnson, ,Matrix Analysis, Cambridge University Press, Cambridge (1985).
[10] H. Hotelling, Some improvement in weighing and other experimental techniques, Ann. Math. Start.16,(1944) p.294-300
[11] Y. J. Ionin, Applying balanced generalized weighing matrices to construct block designs ,The electronic journal of combinatorics 8 (2001)
[12] Ji-Woong Jang, Sang-Hyokim, Jong- Seon No, Habong chung, New Construction of Quaternary Hadamard matrices , International Conference on Sequance and their applications part of the Lecture Notes in Computer Science Vol. No.-3486(2004)361-372.
[13] C. Koukouvinos, Jennifer Seberry, Weighing matrices and their applications , Journal of statistical planning Inference 62 (1997)91-101.[14] C. Kravvaritis, and M. Mitrouli, Compound Matrices: Properties, Numerical issues and analytical computations, Springer Science +Bussiness Media LLC(2008).
[15] D. Raghavrao, Construction and Combinatorial problems in design of experiments, Wiley Series Probability and Statistics, John Wiley and Sons,Inc,NewYork-London Sydney-Toronto (1971)
[16] F.R. Sharpe, The maximum value of a determinant, Bull. Am. Math. Soc. 14(1907) 121-123.
[17] M.K.Singh, and G. Prajapati, Some 2-Weighing matrices from a Hadamard matrix, Acta Ciencia Indica,Vol-XLIIM No.4,273(2016)
[18] M.K. Singh, S.Singh and S.K. Singh , On the construction of weighing matrix , International Journal of research and reviews in Computer Science Vol. No.-4(2010) 99-102.
[19] M.K.Singh and S.N. Topno, , Anticirculant Structured block Weighing matrices from Williamson matrices, International Journal of Mathematics Trend and Technology, Vol-52 No-4(2017)
[20] S. Singh , M.K. Singh , and D.K. Singh , Complex Hadamard matrices and weighing matrices, Journal of Computer Science Vol. No.-4(2010)1492-1497.

Citation :

Gopal Prajapati, Mithilesh Kumar Singh, "Some Infinite Series of Weighing Matrices From Hadamard Matrices," International Journal of Mathematics Trends and Technology (IJMTT), vol. 54, no. 3, pp. 217-221, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V54P523