nach oben

Designs, Codes and Cryptography

Erschienen in:

01.04.2016

Self-dual codes from extended orbit matrices of symmetric designs

verfasst von: Dean Crnković, Sanja Rukavina

Erschienen in: Designs, Codes and Cryptography | Ausgabe 1/2016

Einloggen, um Zugang zu erhalten

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

search-config

KI-gestützte Suche

Aus

Abstract

In this paper we study codes spanned by the rows of an orbit matrix of a symmetric design with respect to the action of an automorphism group that acts with all orbits of the same length. We define an extended orbit matrix and show that under some condition the rows of the extended orbit matrix span a code that is self-dual with respect to a certain scalar product. Further, we show that sometimes a chain of codes can be used to associate a self-dual code to an orbit matrix of a symmetric design.

Vorheriger Artikel Structural cryptanalysis of McEliece schemes with compact keys

Nächster Artikel Self-updatable encryption with short public parameters and its extensions

Assmus E.F. Jr., Key J.D.: Designs and their codes. In: Cambridge Tracts in Mathematics, vol. 103. Cambridge University Press, Cambridge (1992) (Second printing with corrections, 1993)

Beth T., Jungnickel D., Lenz H.: Design Theory, 2nd edn. Cambridge University Press, Cambridge (1999).

Ćepulić V.: On symmetric block designs (45,12,3) with automorphisms of order 5. Ars Comb. 37, 33–48 (1994).

Crnković D., Rukavina S.: Construction of block designs admitting an abelian automorphism group. Metrika 62, 175–183 (2005).

Crnković D., Rodrigues B.G., Rukavina S., Simčić L.: Self-orthogonal codes from orbit matrices of 2-designs. Adv. Math. Commun. 7, 161–174 (2013).

Harada M., Tonchev V.D.: Self-orthogonal codes from symmetric designs with fixed-point-free automorphisms. Discret. Math. 264, 81–90 (2003).

Janko Z.: Coset enumeration in groups and constructions of symmetric designs. Combinatorics ’90 (Gaeta, 1990). Ann. Discret. Math. 52, 275–277 (1992).

Lander E.: Symmetric Designs: An Algebraic Approach. Cambridge University Press, Cambridge (1983).

Tonchev V.D.: Codes. In: Colbourn C.J., Dinitz J.H. (eds.) Handbook of Combinatorial Designs, 2nd ed., pp. 667–702. Chapman & Hall/CRC Press, Boca Raton (2007).

10.

Wilson R.M.: Codes and modules associated with designs and \(t\)-uniform hypergraphs. In: Crnković D., Tonchev V.D. (eds.) Information Security, Coding Theory and Related Combinatorics. NATO Science for Peace and Security Series—D: Information and Communication Security, vol. 29, pp. 404–436. IOS, Amsterdam (2011).

Titel: Self-dual codes from extended orbit matrices of symmetric designs
verfasst von: Dean Crnković
Sanja Rukavina
Publikationsdatum: 01.04.2016
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 1/2016
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-015-0038-x

Springer Professional

Self-dual codes from extended orbit matrices of symmetric designs

Abstract

Premium Partner

Springer Professional

Abstract

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

Weitere Artikel der Ausgabe 1/2016

Effective compression maps for torus-based cryptography

Binary codes of the symplectic generalized quadrangle of even order

An efficient IBE scheme with tight security reduction in the random oracle model

Structural cryptanalysis of McEliece schemes with compact keys

Self-updatable encryption with short public parameters and its extensions

On the automorphisms of order 15 for a binary self-dual code

Premium Partner