Abstract
We explore some links between higher weights of binary codes based on entropy/length profiles and the asymptotic rate of (2,1)-separating codes. These codes find applications in digital fingerprinting and broadcast encryption for example. We conjecture some bounds on the higher weights, whose proof would considerably strengthen the upper bound on the rate of (2,1)-separating codes.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bassalygo, L.A.: Supports of a code. In: Giusti, M., Cohen, G., Mora, T. (eds.) AAECC 1995. LNCS, vol. 948. Springer, Heidelberg (1995)
Blackburn, S.R.: Frameproof codes. SIAM J. Discrete Math. 16(3), 499–510 (2003)
Boneh, D., Shaw, J.: Collusion-secure fingerprinting for digital data. CRYPTO 1995 44(5), 1897–1905 (1998), Presented in part at CRYPTO 1995 (1995)
Cohen, G., Litsyn, S., Zémor, G.: Upper bounds on generalized distances. IEEE Trans. Inform. Theory 40(6), 2090–2092 (1994)
Cohen, G., Zémor, G.: Intersecting codes and independent families. IEEE Trans. Inform. Theory 40, 1872–1881 (1994)
Cohen, G.D., Encheva, S.B., Litsyn, S., Schaathun, H.G.: Intersecting codes and separating codes. Discrete Applied Mathematics 128(1), 75–83 (2003)
Cohen, G.D., Encheva, S.B., Schaathun, H.G.: More on (2,2)-separating codes. IEEE Trans. Inform. Theory 48(9), 2606–2609 (2002)
Cohen, G.D., Schaathun, H.G.: Asymptotic overview on separating codes. Technical Report 248, Dept. of Informatics, University of Bergen (May 2003), Available at http://www.ii.uib.no/publikasjoner/texrap/index.shtml
Helleseth, T., Kløve, T., Mykkeltveit, J.: The weight distribution of irreducible cyclic codes with block lengths n_1((q l − 1)/n). Discrete Math. 18, 179–211 (1977)
Körner, J.: On the extremal combinatorics of the Hamming space. J. Combin. Theory Ser. A 71(1), 112–126 (1995)
Krasnopeev, A., Sagalovich, Y.L.: The Kerdock codes and separating systems. In: Eight International Workshop on Algebraic and Combinatorial Coding Theory (2002)
McEliece, R.J., Rodemich, E.R., Rumsey, H., Rumsey Jr., H., Welch, L.R.: New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities. IEEE Trans. Inform. Theory IT-23(2), 157–166 (1977)
Reuven, I., Be’ery, Y.: Entropy/length profiles, bounds on the minimal covering of bipartite graphs, and the trellis complexity of nonlinear codes. IEEE Trans. Inform. Theory 44(2), 580–598 (1998)
Reuven, I., Be’ery, Y.: Generalized Hamming weights of nonlinear codes and the relation to the Z 4-linear representation. IEEE Trans. Inform. Theory 45(2), 713–720 (1999)
Sagalovich, Y.L.: Separating systems. Problems of Information Transmission 30(2), 105–123 (1994)
Staddon, J.N., Stinson, D.R., Wei, R.: Combinatorial properties of frameproof and traceability codes. IEEE Trans. Inform. Theory 47(3), 1042–1049 (2001)
Wei, V.K.: Generalized Hamming weights for linear codes. IEEE Trans. Inform. Theory 37(5), 1412–1418 (1991)
Xing, C.: Asymptotic bounds on frameproof codes. IEEE Trans. Inform. Theory 40(11), 2991–2995 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schaathun, H.G., Cohen, G.D. (2005). A Trellis-Based Bound on (2,1)-Separating Codes. In: Smart, N.P. (eds) Cryptography and Coding. Cryptography and Coding 2005. Lecture Notes in Computer Science, vol 3796. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11586821_5
Download citation
DOI: https://doi.org/10.1007/11586821_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30276-6
Online ISBN: 978-3-540-32418-8
eBook Packages: Computer ScienceComputer Science (R0)