nach oben

Designs, Codes and Cryptography

Erschienen in:

01.12.2014

Extremal properties of t-SEEDs and recursive constructions

verfasst von: Yiling Lin, Masakazu Jimbo

Erschienen in: Designs, Codes and Cryptography | Ausgabe 3/2014

Einloggen, um Zugang zu erhalten

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

A t-spontaneous emission error design, called t-SEED for short, is a combinatorial design introduced by Beth et al. (Des Codes Cryptogr 29:51–70, 2003) in relation to a quantum jump code. In this article, firstly, it is shown that an optimal t-SEED attaining a given upper bound is a large set of Steiner t-designs. Secondly, we present some recursive constructions of t-SEEDs. Moreover, an application to secret sharing scheme by utilizing the properties of a t-SEED is also discussed.

Vorheriger Artikel New optimal constructions of conflict-avoiding codes of odd length and weight 3

Nächster Artikel Difference sets with few character values

Alber G., Beth T., Charnes C., Delgado A., Grassl M., Mussinger M.: Stabilizing distinguishable qubits against spontaneous decay by detected-jump correcting quantum codes. Phys. Rev. Lett. 86, 4402–4405 (2001).

Alber G., Beth T., Charnes C., Delgado A., Grassl M., Mussinger M.: Detected-jump-error-correcting quantum codes, quantum error designs and quantum computation. Phys. Rev. A 68, 012316 (2003).

Baranyai Z.: On the factorizations of the complete uniform hypergraph. Finite and infinite sets. Colloq. Math. Soc. Janos Bolyai, vol. 10, pp. 91–108. North-Holland, Amsterdam (1975)

Blakley G.R.: Safeguarding cryptographic keys. AFIPS Conf. Proc. 48, 313–317 (1979).

Beth T., Charnes C., Grassl M., Alber G., Delgado A., Mussinger M.: A new class of designs which protect against quantum jumps. Des. Codes Cryptogr. 29, 51–70 (2003).

Calderbank A.R., Shor P.W.: Good quantum error-correcting codes exist. Phys. Rev. A. 54, 1098–1105 (1996).

Calderbank A.R., Rains E.M., Shor P.W., Sloane N.J.A.: Quantum error correction via codes over \(GF(4)\). IEEE Trans. Inf. Theory 44, 1369–1387 (1998).

Cayley A.: On the triadic arrangements of seven and fifteen things. Lond. Edinb. Dublin Philos. Mag. J. Sci. 37, 50–53 (1850).

Chouinard L.G.: Partitions of the 4-subsets of a 13-set into disjoint projective planes. Discret. Math. 45, 297–300 (1983).

10.

Chen D., Stinson D.R.: Recent results on combinatorial constructions for threshold schemes. Australas. J. Comb. 1, 29–48 (1990).

11.

Deng Y.P., Guo L.F., Liu M.L.: Constructions for Anonymous secret sharing schemes using combinatorial designs. Acta Math. Appl. Sin. Engl. Ser. 23(1), 67–78 (2007).

12.

Ekert A., Macchiavello C.: Quantum error correction for communication. Phys. Rev. Lett. 77, 2585–2588 (1996).

13.

Hartman A.: Halving the complete design. Ann. Discret. Math. 34, 207–224 (1987).

14.

Jimbo M., Shiromoto K.: Quantum jump codes and related combinatorial designs. In: Crnkovic‘ D., Tonchev V. (eds.) Information Security, Coding Theory and Related Combinatorics, vol. 29, pp. 285–311. IOS Press, Amsterdam (2011).

15.

Khosrovshahi G.B., Tayfeh-Rezaie B.: Large sets of \(t\)-designs through partitionable sets: a survey. Discret. Math. 306, 2993–3004 (2006).

16.

Lu J.X.: On large sets of disjoint Steiner triple systems I, II and III. J. Comb. Theory Ser. A 37, 140–182 (1983).

17.

Lu J.X.: On large sets of disjoint Steiner triple systems IV, V and VI. J. Comb. Theory Ser. A 37, 136–192 (1984).

18.

Mathon R.A.: Searching for spreads and packings. In: Hirschfeld J.W.P., Magliveras S.S., de Resmini M.J. (eds.) Geometry, Combinatorial Designs and Related Structures, London Math. Soc. Lecture Note Ser. (Spetses 1996) vol. 245, pp. 161–176. Cambridge University Press, Cambridge (1997).

19.

Miao Y.: A combinatorial characterization of regular anonymous perfect threshold schemes. Inf. Process. Lett. 85, 131–135 (2003).

20.

Raghavarao D.: Constructions and Combinatorial Problems in Design of Experiments. Wiley, New York (1971).

21.

Shamir A.: How to share a secret. Commun. ACM 22, 612–613 (1979).

22.

Steane A.: Multiple particle interference and quantum error correction. Proc. R. Soc. Lond. A 452, 2551–2577 (1996).

23.

Steane A.M.: Error correcting codes in quantum theory. Phys. Rev. Lett. 77, 793–797 (1996).

24.

Shor P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, 2493–2496 (1995).

25.

Stinson D.R., Vanstone S.A.: A combinatorial approach to threshold schemes. SIAM J. Discret. Math. 1, 230–237 (1988).

26.

Schellenberg P.J., Stinson D.R.: Threshold schemes from combinatorial designs. J. Comb. Math. Comb. Comput. 5, 143–160 (1989).

27.

Schreiber S.: Some balanced complete block designs. Israel J. Math. 18, 31–37 (1874).

28.

Schreiber S.: Covering all triples on \(n\) marks by disjoint Steiner systems. J. Comb. Theory Ser. A 15, 347–350 (1973).

29.

Teirlinck L.: On the maximum number of disjoint triple systems. J. Geom. 12, 93–96 (1975).

30.

Teirlinck L.: A completion of Lu’s determination of the spectrum of large sets of disjoint Steiner Triple systems. J. Comb. Theory Ser. A 57, 302–305 (1991).

Titel: Extremal properties of t-SEEDs and recursive constructions
verfasst von: Yiling Lin
Masakazu Jimbo
Publikationsdatum: 01.12.2014
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 3/2014
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-013-9829-0

Springer Professional

Extremal properties of t-SEEDs and recursive constructions

Abstract

Premium Partner

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Weitere Artikel der Ausgabe 3/2014

Linear algebraic techniques to construct monochrome visual cryptographic schemes for general access structure and its applications to color images

Erratum to: Linear covering codes and error-correcting codes for limited-magnitude errors

The weight distributions of some cyclic codes with three or four nonzeros over

Any network code comes from an algebraic curve taking osculating spaces

Cameron–Liebler line classes in

A construction for t-fold perfect authentication codes with arbitration

Premium Partner