Two-level Cretan matrices constructed using SBIBD

• Autorzy: N. A. Balonin , Jennifer Seberry
• 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.

Słowa kluczowe

EN

Hadamard matrices; orthogonal matrices; Cretan matrices; symmetric balanced incomplete blockdesigns (SBIBD); difference sets

Kategorie tematyczne

• 05B20: Matrices (incidence, Hadamard, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-03-17

zaakceptowano

2015-07-25

online

2015-08-04

Twórcy

autor

N. A. Balonin

• Saint Petersburg State University of Aerospace Instrumentation, 67, B. Morskaia St., 190000, St. Petersburg,
  Russian Federation

autor

Jennifer Seberry

• 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. Informatsionnoupravliaiushchie sistemy, 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: A Collection of Surveys, J. H. Dinitz and D. R. Stinson, eds., John Wiley and Sons, Inc., 1992. pp. 431–560.

Identyfikatory

DOI

10.1515/spma-2015-0017