Top

Designs, Codes and Cryptography

Published in:

18-08-2016

Doubly resolvable Steiner quadruple systems and related designs

Author: Zhaoping Meng

Published in: Designs, Codes and Cryptography | Issue 3/2017

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Two resolutions of the same \(\hbox {SQS}(v)\) are said to be orthogonal, when each parallel class of one resolution has at most one block in common with each parallel class of the other resolution. If an \(\hbox {SQS}(v)\) has two orthogonal resolutions, the \(\hbox {SQS}(v)\) is called a doubly resolvable \(\hbox {SQS}(v)\). In this paper, we use a quadrupling construction to obtain an infinite class of doubly resolvable Steiner quadruple systems. We also give some results of doubly resolvable H designs and doubly resolvable candelabra quadruple systems.

previous article Cryptanalysis of multilinear maps from ideal lattices: revisited

next article The BEL-rank of finite semifields

Booth T.R.: A resolvable quadruple system of order 20. Ars Comb. 5, 121–125 (1978).

de Vries H.L.: On orthogonal resolutions of the classical Steiner quadruple system SQS(16). Des. Codes Cryptogr. 48, 287–292 (2008).

Greenwell D.L., Lindner C.C.: Some remarks on resolvable quadruple systems. Ars Comb. 6, 215–221 (1978).

Hanani H.: On quadruple systems. Can. J. Math. 12, 145–157 (1960).

Hartman A.: Resolvable Steiner quadruple systems. Ars Comb. 9, 263–273 (1980).

Hartman A.: Tripling quadruple systems. Ars Comb. 10, 255–309 (1980).

Hartman A.: Doubly and orthogonally resolvable quadruple systems. Ars Comb. In: Combinatorial Mathematics, VII. Proceedings of Seventh Australian Conference. Lecture Notes in Mathematics. University of Newcastle, Newcastle, 1979, vol. 829, pp. 157–164. Springer, Berlin (1980).

Hartman A.: The existence of resolvable Steiner quadruple systems. J. Comb. Theory (A) 44, 182–206 (1987).

Hartman A., Phelps K.T.: Steiner quadruple systems. In: Dinitz J.H., Stinson D.R. (eds.) Contemporary Design Theory, pp. 205–240. Wiley, New York (1992).

10.

Ji L.: An improvement on H design. J. Comb. Des. 17, 25–35 (2009).MathSciNetCrossRefMATH

11.

Ji L., Zhu L.: Resolvable Steiner quadruple systems for the last 23 orders. SIAM J. Discret. Math. 19, 420–432 (2005).MathSciNetCrossRefMATH

12.

Mills W.H.: On the existence of H designs. Congr. Numer. 79, 129–141 (1990).

13.

Zhang S.: On candelabra quadruple systems. Ars Comb. 99, 335–352 (2011).

14.

Zhang X., Ge G.: H-designs with the properties of resolvability or (1,2)-resolvability. Des. Codes Cryptogr. 55, 81–101 (2010).

15.

Zhang S., Ji L., Song G.: Some new infinite classes of candelabra quadruple systems. J. Comb. Des. 24, 5–20 (2016).

Title: Doubly resolvable Steiner quadruple systems and related designs
Author: Zhaoping Meng
Publication date: 18-08-2016
Publisher: Springer US
Published in: Designs, Codes and Cryptography / Issue 3/2017
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-016-0269-5

Springer Professional

Doubly resolvable Steiner quadruple systems and related designs

Abstract

Premium Partner

Springer Professional

Abstract

Please log in to get access to your license.

Other articles of this Issue 3/2017

Near-complete external difference families

Construction of low-hit-zone frequency hopping sequences with optimal partial Hamming correlation by interleaving techniques

Higher order differentiation over finite fields with applications to generalising the cube attack

The BEL-rank of finite semifields

Quantum MDS codes with relatively large minimum distance from Hermitian self-orthogonal codes

Galois self-dual constacyclic codes

Premium Partner