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2008 | 28 | 2 | 183-207
Tytuł artykułu

Certain new M-matrices and their properties with applications

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The Mₙ-matrix was defined by Mohan [21] who has shown a method of constructing (1,-1)-matrices and studied some of their properties. The (1,-1)-matrices were constructed and studied by Cohn [6], Ehrlich [9], Ehrlich and Zeller [10], and Wang [34]. But in this paper, while giving some resemblances of this matrix with a Hadamard matrix, and by naming it as an M-matrix, we show how to construct partially balanced incomplete block designs and some regular graphs by it. Two types of these M-matrices have been considered. Also we will make a mention of certain applications of these M-matrices in signal and communication processing, and network systems and end with some open problems.
Twórcy
  • Sir CRR Institute of Mathematics, Eluru-534007, AP, India
  • Hiroshima Institute of Technology, Hiroshima 731-5193, Japan
autor
  • Institute of Information & Communication, Chonbuk National University, Korea
autor
  • Center for Combinatorics, Nankai University, Tianjin-300071, PR China
Bibliografia
  • [1] B.E. Aupperle and J.F. Meyer, Fault-tolerant BIBD networks, Proc. Inter. Symp. (FTCS) 18, IEEE, (1988), 306-311.
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  • [3] R.C. Bose, Strongly regular graphs, partial geometries and partially balanced designs, Pacific J. Math. 13 (1963), 389-419.
  • [4] R.C. Bose and K.R. Nair, Partially balanced incomplete block designs, Sankhyā 4 (1939), 337-372.
  • [5] Y. Chang, Y. Hua, X.G. Xia and B. Sudler, An insight into space-time block codes using Hurwitz-Random families of matrices, (personal communication) 2005.
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  • [9] H. Ehlich, Determinantenabschätzungen für binäre matrizen, Math. Z. 83 (1964), 123-132.
  • [10] H. Ehlich and K. Zeller, Binäre matrizen, Z. Angew. Math. Mech. 42 (1962), 20-21.
  • [11] P. Fan and M. Darnell, Sequence Design for Communications Applications, Research Studies Press Ltd., Wiley, New York 1996.
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  • [13] J.M. Goethals and J.J. Seidel, Strongly regular graphs derived from combinatorial designs, Can. J. Math. 22 (1970), 597-614.
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  • [15] H. Jafarkhani, A quasi-orthogonal space-time block code, Preprint 2001.
  • [16] S. Kageyama and R.N. Mohan, On μ-resolvable BIB designs, Discrete Math. 45 (1983), 113-121.
  • [17] S. Kageyama and R.N. Mohan, On the construction of group divisible partially balanced incomplete block designs, Bull. Fac. Sch. Edu., Hrioshima Univ. 7 (1984), 57-60.
  • [18] J. Kahn, J. Komlos and E. Szemeredi, On the probability that a random ± 1 matrix is singular, J. Amer. Math. Soc. 8 (1995), 223-240.
  • [19] C.-W. Liu, A method of constructing certain symmetric partially balanced designs, Scientia Sinica 12 (1963), 1935-1936.
  • [20] R.N. Mohan, A new series of μ-resolvable (d+1)-associate class GDPBIB designs, Indian J. Pure Appl. Math. 30 (1999), 89-98.
  • [21] R.N. Mohan, Some classes of Mₙ-matrices and Mₙ-graphs and applications, JCISS 26 (2001), 51-78.
  • [22] R.N. Mohan and P.T. Kulkarni, A new family of fault-tolerant M-networks, IEEE Trans. Comupters (under revision) (2006).
  • [23] N.C. Nguyen, N.M.D. Vo and S.Y. Lee, Fault tolerant routing and broadcasting in deBruijn networks, Advanced Information Networking and Applications, AINA 2005, 19th International Conference, March 2005, 2 (2005), 35-40.
  • [24] D. Raghavarao, A generalization of group divisible designs, Ann. Math. Statist. 31 (1960), 756-771.
  • [25] D. Raghavarao, Constructions and Combinatorial Problems in Design of Experiments, Wiley, New York 1971.
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  • [27] J. Seberry and M. Yamada, Hadamard Matrices, Sequences and Block Designs, Contemporary Design Theory: A Collection of Surveys (edited by J.H. Dinitz and D.R. Stinson), Wiley, New York 1992, 431-560.
  • [28] N. Seifer, Upper bounds for permanent of (1,-1)-matrices, Isreal J. Math. 48 (1984), 69-78.
  • [29] S.S. Shrikhande, Cyclic solutions of symmetric group divisible designs, Calcutta Statist. Assoc. Bull. 5 (1953), 36-39.
  • [30] D.B. Skillicorn, A new class of fault-tolerant static interconnection networks, IEEE Trans. Comupters 37 (1988), 1468-1470.
  • [31] D.A. Sprott, A series of symmetric group divisible designs, Ann. Math. Statist. 30 (1959), 249-251.
  • [32] M.R. Teague, Image analysis via the general theory of moments, J. Optical Soc. America 70 (1979), 920-930.
  • [33] B. Vasic and O. Milenkovic, Combinatorial constructions of low-density parity-check codes for iterative decoding, IEEE Trans. on Information Theory 50 (2004), 1156-1176.
  • [34] E.T. Wang, On permanents of (1,-1)-matrices, Isreal J. Math. 18 (1974), 353-361.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1100
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