# 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

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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

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