nach oben

Designs, Codes and Cryptography

Erschienen in:

01.09.2015

Plateaued functions and one-and-half difference sets

verfasst von: Oktay Olmez

Erschienen in: Designs, Codes and Cryptography | Ausgabe 3/2015

Einloggen, um Zugang zu erhalten

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

search-config

KI-gestützte Suche

Aus

Abstract

We construct an infinite family of \(1\frac{1}{2}\)-difference sets in non-cyclic abelian \(p\)-groups. In particular, we examine the construction in \(2\)-groups to discover the useful relationship between \(1\frac{1}{2}\)-difference sets and certain Boolean functions.

Vorheriger Artikel Codes over rings and Hermitian lattices

Nächster Artikel Diagonally cyclic equitable rectangles

It is often known as a tactical configuration.

Bose [2] studied \(1\frac{1}{2}\)-designs and called them partial geometric designs.

Beth T., Jungnickel D., Lenz H.: Design Theory I, vol. 69. Cambridge University Press, Cambridge (1999).

Bose R.C., Shrikhande S.S., Singhi N.M.: Edge regular multigraphs and partial geometric designs with an application to the embedding of quasi-residual designs. Colloq. Int. sulle Teorie Comb. 1, 49–81 (1976).

Canteaut A., Charpin P.: Decomposing bent functions. IEEE Trans. Inf. Theory 49(8), 2004–2019 (2003).

Canteaut A., Carlet C., Charpin P., Fontaine C.: On cryptographic properties of the cosets of r (1, m). IEEE Trans. Inf. Theory 47(4), 1494–1513 (2001).

Carlet C.: Partially-bent functions. Des. Codes Cryptogr. 3(2), 135–145 (1993).

Carlet C.: Boolean functions for cryptography and error correcting codes. Boolean Models Methods Math. Comput. Sci. Eng. 2, 257 (2010).

Carlet C., Prouff E.: On plateaued functions and their constructions. In: Johansson T. (ed.) Fast Software Encryption, pp 54–73. Springer, Berlin (2003).

Chee S., Lee S., Kim K.: Semi-bent functions. In: Pieprzyk J., Safavi-Naini R. (eds.) Advances in Cryptology-ASIACRYPT’94, pp. 105–118. Springer, Berlin (1995).

Chung F.R.K., Salehi J.A., Wei V.K.: Optical orthogonal codes: design, analysis and applications. IEEE Trans. Inf. Theory 35(3), 595–604 (1989).

10.

Dillon J.F.: Elementary Hadamard difference sets. Ph.D. thesis, University of Maryland, College Park, MD (1974).

11.

Dillon J.F., McGuire G.: Near bent functions on a hyperplane. Finite Fields Appl. 14(3), 715–720 (2008).

12.

Jungnickel D., Pott A.: Perfect and almost perfect sequences. Discret. Appl. Math. 95(1–3), 331–360 (1999).

13.

McFarland R.L.: A family of difference sets in non-cyclic groups. J. Comb. Theory A 15(1), 1–10 (1973).

14.

Neumaier A.: \(t\frac{1}{2}\)-designs. J. Comb. Theory A 28(3), 226–248 (1980).

15.

Olmez O.: Symmetric \(1\frac{1}{2}\)-designs and \(1\frac{1}{2}\)-difference sets. Comb. Des. Theory (2013). doi:10.1002/jcd.21354.

16.

Vasic B., Milenkovic O.: Combinatorial constructions of low-density parity-check codes for iterative decoding. IEEE Trans. Inf. Theory 50(6), 1156–1176 (2004).

17.

Zheng Y., Zhang X.: Plateaued functions. In: Varadharajan V., Mu Y. (eds.) Information and Communication Security, pp. 284–300. Springer, Berlin (1999).

Titel: Plateaued functions and one-and-half difference sets
verfasst von: Oktay Olmez
Publikationsdatum: 01.09.2015
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 3/2015
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-014-9975-z

Springer Professional

Abstract

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

Weitere Artikel der Ausgabe 3/2015

Almost universal forgery attacks on AES-based MAC’s

An investigation of the tangent splash of a subplane of

On the automorphisms of designs constructed from finite simple groups

Bentness and nonlinearity of functions on finite groups

Practical-time attacks against reduced variants of MISTY1

Diagonally cyclic equitable rectangles