Two-level Cretan matrices constructed using SBIBD
N. A. Balonin; Jennifer Seberry
Special Matrices (2015)
- Volume: 3, Issue: 1, page 186-192, electronic only
- ISSN: 2300-7451
Access Full Article
top
Abstract
topHow to cite
topN. A. Balonin, and Jennifer Seberry. "Two-level Cretan matrices constructed using SBIBD." Special Matrices 3.1 (2015): 186-192, electronic only. <http://eudml.org/doc/271757>.
@article{N2015,
abstract = {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.},
author = {N. A. Balonin, Jennifer Seberry},
journal = {Special Matrices},
keywords = {Hadamard matrices; orthogonal matrices; Cretan matrices; symmetric balanced incomplete block
designs (SBIBD); difference sets; cretan matrices; symmetric balanced incomplete block designs (SBIBD)},
language = {eng},
number = {1},
pages = {186-192, electronic only},
title = {Two-level Cretan matrices constructed using SBIBD},
url = {http://eudml.org/doc/271757},
volume = {3},
year = {2015},
}
TY - JOUR
AU - N. A. Balonin
AU - Jennifer Seberry
TI - Two-level Cretan matrices constructed using SBIBD
JO - Special Matrices
PY - 2015
VL - 3
IS - 1
SP - 186
EP - 192, electronic only
AB - 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.
LA - eng
KW - Hadamard matrices; orthogonal matrices; Cretan matrices; symmetric balanced incomplete block
designs (SBIBD); difference sets; cretan matrices; symmetric balanced incomplete block designs (SBIBD)
UR - http://eudml.org/doc/271757
ER -
References
top- [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. Zbl25.0221.02
- [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. Zbl0776.05028
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.