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Two-level Cretan matrices constructed using SBIBD

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Two-level Cretan matrices are orthogonal matrices with two elements, x and y. At least one element per row and column is 1 and the other element has modulus ≤ 1. These have been studied in the Russian literature for applications in image processing and compression. Cretan matrices have been found by both mathematical and computational methods but this paper concentrates on mathematical solutions for the first time. We give, for the first time, families of Cretan matrices constructed using the incidence matrix of a symmetric balanced incomplete block design and Hadamard related difference sets.
Wydawca
Czasopismo
Rocznik
Tom
3
Numer
1
Opis fizyczny
Daty
otrzymano
2015-03-17
zaakceptowano
2015-07-25
online
2015-08-04
Twórcy
  • Saint Petersburg State University of Aerospace Instrumentation, 67, B. Morskaia St., 190000, St. Petersburg,
    Russian Federation
  • School of Computing and Information Technology, Faculty of Engineering and
    Information Sciences, University of Wollongong, NSW 2522, Australia
Bibliografia
  • [1] N. A. Balonin. Existence of Mersenne Matrices of 11th and 19th Orders. Informatsionno-upravliaiushchie sistemy, 2013. 2, pp. 89 – 90 (In Russian).
  • [2] N. A. Balonin and L. A. Mironovski. Hadamard matrices of odd order, Informatsionno-upravliaiushchie sistemy, 2006.3,pp. 46–50 (In Russian).
  • [3] N. A. Balonin and Jennifer Seberry. Remarks on extremal and maximum determinant matrices with real entries ≤ 1.Informatsionno-upravliaiushchie sistemy, 5, (71) (2014), p2–4. (In English).
  • [4] N. A. Balonin and M. B. Sergeev. On the issue of existence of Hadamard and Mersenne matrices. Informatsionnoupravliaiushchiesistemy, 2013. 5 (66), pp. 2–8 (In Russian).
  • [5] J. Hadamard, Résolution d’une question relative aux déterminants. Bulletin des Sciences Mathematiques. 1893. Vol. 17. pp.240-246.
  • [6] La Jolla Difference Set Repository. URL www.ccrwest.org/ds.html. Viewed 2014:10:03.
  • [7] Jennifer Seberry and Mieko Yamada. Hadamard matrices, sequences, and block designs, Contemporary Design Theory: ACollection of Surveys, J. H. Dinitz and D. R. Stinson, eds., John Wiley and Sons, Inc., 1992. pp. 431–560.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_spma-2015-0017
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