On the resolutions of cyclic Steiner triple systems with small parameters

Volume: 3 Number: 3 August 9, 2016
  • Svetlana Topalova
EN

On the resolutions of cyclic Steiner triple systems with small parameters

Abstract

The paper presents useful invariants of resolutions of cyclic $STS(v)$ with $v\le 39$, namely of all resolutions of cyclic $STS(15)$, $STS(21)$ and $STS(27)$, of the resolutions with nontrivial automorphisms of cyclic $STS(33)$ and of resolutions with automorphisms of order $13$  of cyclic $STS(39)$.

References

  1. T. Baicheva, S. Topalova, Classification results for (v, k, 1) cyclic difference families with small parameters, Mathematics of Distances and Applications. M. Deza, M. Petitjean, K. Markov (Eds.), in International book series: Information Science and Computing, 25 (2012), 24–30.
  2. T. Beth, D. Jungnickel, H. Lenz, Design Theory, Cambridge University Press, Cambridge, 1993.
  3. C. J. Colbourn, J. H. Dinitz (Eds.), The CRC Handbook of Combinatorial Designs, CRC Press, Boca Raton, FL, 2007.
  4. C. J. Colbourn, J. H. Dinitz, D. R. Stinson, Applications of Combinatorial Designs to Communications, Cryptography, and Networking, Surveys in Combinatorics, 1999, Edited by J. D. Lamb and D. A. Preece, London Mathematical Society Lecture Note Series 267 (1999), 37–100.
  5. C. J. Colbourn, S. S. Magliveras, R. A. Mathon, Transitive Steiner and Kirkman triple systems of order 27, Math. Comp. 58(197) (1992) 441–449.
  6. M. J. Colbourn, R. A. Mathon, On cyclic Steiner 2-designs. Topics on Steiner systems, Ann. Discret Math. 7 (1980) 215–253.
  7. M. Genma, M. Mishima, M. Jimbo, Cyclic resolvability of cyclic Steiner 2-designs, J. Combin. Des. 5(3) (1997) 177–187.
  8. A. Gruner, M. Huber, New combinatorial construction techniques for low-density parity-check codes and systematic repeat-accumulate codes, IEEE Trans. Commun. 60(9) (2012) 2387–2395.

Details

Primary Language

English

Subjects

-

Journal Section

-

Authors

Svetlana Topalova This is me

Publication Date

August 9, 2016

Submission Date

August 8, 2016

Acceptance Date

-

Published in Issue

Year 2016 Volume: 3 Number: 3

APA
Topalova, S. (2016). On the resolutions of cyclic Steiner triple systems with small parameters. Journal of Algebra Combinatorics Discrete Structures and Applications, 3(3), 201-208. https://doi.org/10.13069/jacodesmath.47635
AMA
1.Topalova S. On the resolutions of cyclic Steiner triple systems with small parameters. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016;3(3):201-208. doi:10.13069/jacodesmath.47635
Chicago
Topalova, Svetlana. 2016. “On the Resolutions of Cyclic Steiner Triple Systems With Small Parameters”. Journal of Algebra Combinatorics Discrete Structures and Applications 3 (3): 201-8. https://doi.org/10.13069/jacodesmath.47635.
EndNote
Topalova S (August 1, 2016) On the resolutions of cyclic Steiner triple systems with small parameters. Journal of Algebra Combinatorics Discrete Structures and Applications 3 3 201–208.
IEEE
[1]S. Topalova, “On the resolutions of cyclic Steiner triple systems with small parameters”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 3, no. 3, pp. 201–208, Aug. 2016, doi: 10.13069/jacodesmath.47635.
ISNAD
Topalova, Svetlana. “On the Resolutions of Cyclic Steiner Triple Systems With Small Parameters”. Journal of Algebra Combinatorics Discrete Structures and Applications 3/3 (August 1, 2016): 201-208. https://doi.org/10.13069/jacodesmath.47635.
JAMA
1.Topalova S. On the resolutions of cyclic Steiner triple systems with small parameters. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016;3:201–208.
MLA
Topalova, Svetlana. “On the Resolutions of Cyclic Steiner Triple Systems With Small Parameters”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 3, no. 3, Aug. 2016, pp. 201-8, doi:10.13069/jacodesmath.47635.
Vancouver
1.Svetlana Topalova. On the resolutions of cyclic Steiner triple systems with small parameters. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016 Aug. 1;3(3):201-8. doi:10.13069/jacodesmath.47635