6,398 research outputs found
Constructing Optimal Authentication Codes with Perfect Multi-fold Secrecy
We establish a construction of optimal authentication codes achieving perfect
multi-fold secrecy by means of combinatorial designs. This continues the
author's work (ISIT 2009) and answers an open question posed therein. As an
application, we present the first infinite class of optimal codes that provide
two-fold security against spoofing attacks and at the same time perfect two-
fold secrecy.Comment: 4 pages (double-column); to appear in Proc. 2010 International Zurich
Seminar on Communications (IZS 2010, Zurich
Coding Theory and Algebraic Combinatorics
This chapter introduces and elaborates on the fruitful interplay of coding
theory and algebraic combinatorics, with most of the focus on the interaction
of codes with combinatorial designs, finite geometries, simple groups, sphere
packings, kissing numbers, lattices, and association schemes. In particular,
special interest is devoted to the relationship between codes and combinatorial
designs. We describe and recapitulate important results in the development of
the state of the art. In addition, we give illustrative examples and
constructions, and highlight recent advances. Finally, we provide a collection
of significant open problems and challenges concerning future research.Comment: 33 pages; handbook chapter, to appear in: "Selected Topics in
Information and Coding Theory", ed. by I. Woungang et al., World Scientific,
Singapore, 201
Efficient Two-Stage Group Testing Algorithms for Genetic Screening
Efficient two-stage group testing algorithms that are particularly suited for
rapid and less-expensive DNA library screening and other large scale biological
group testing efforts are investigated in this paper. The main focus is on
novel combinatorial constructions in order to minimize the number of individual
tests at the second stage of a two-stage disjunctive testing procedure.
Building on recent work by Levenshtein (2003) and Tonchev (2008), several new
infinite classes of such combinatorial designs are presented.Comment: 14 pages; to appear in "Algorithmica". Part of this work has been
presented at the ICALP 2011 Group Testing Workshop; arXiv:1106.368
Information Theoretic Authentication and Secrecy Codes in the Splitting Model
In the splitting model, information theoretic authentication codes allow
non-deterministic encoding, that is, several messages can be used to
communicate a particular plaintext. Certain applications require that the
aspect of secrecy should hold simultaneously. Ogata-Kurosawa-Stinson-Saido
(2004) have constructed optimal splitting authentication codes achieving
perfect secrecy for the special case when the number of keys equals the number
of messages. In this paper, we establish a construction method for optimal
splitting authentication codes with perfect secrecy in the more general case
when the number of keys may differ from the number of messages. To the best
knowledge, this is the first result of this type.Comment: 4 pages (double-column); to appear in Proc. 2012 International Zurich
Seminar on Communications (IZS 2012, Zurich
The Classification of Flag-transitive Steiner 4-Designs
Among the properties of homogeneity of incidence structures flag-transitivity
obviously is a particularly important and natural one. Consequently, in the
last decades also flag-transitive Steiner tdesigns (i.e. flag-transitive
t-(v,k,1) designs) have been investigated, whereas only by the use of the
classification of the finite simple groups has it been possible in recent years
to essentially characterize all flag-transitive Steiner 2-designs. However,
despite the finite simple group classification, for Steiner t-designs with
parameters t > 2 such characterizations have remained challenging open problems
for about 40 years (cf. [11, p. 147] and [12, p. 273], but presumably dating
back to around 1965). The object of the present paper is to give a complete
classification of all flag-transitive Steiner 4-designs. Our result relies on
the classification of the finite doubly transitive permutation groups and is a
continuation of the author's work [20, 21] on the classification of all
flag-transitive Steiner 3-designs.Comment: 26 pages; to appear in: "Journal of Algebraic Combinatorics
On the existence of block-transitive combinatorial designs
Block-transitive Steiner -designs form a central part of the study of
highly symmetric combinatorial configurations at the interface of several
disciplines, including group theory, geometry, combinatorics, coding and
information theory, and cryptography. The main result of the paper settles an
important open question: There exist no non-trivial examples with (or
larger). The proof is based on the classification of the finite 3-homogeneous
permutation groups, itself relying on the finite simple group classification.Comment: 9 pages; to appear in "Discrete Mathematics and Theoretical Computer
Science (DMTCS)
The classification of flag-transitive Steiner 3-designs
We solve the long-standing open problem of classifying all 3-(v,k,1) designs
with a flag-transitive group of automorphisms (cf. A. Delandtsheer, Geom.
Dedicata 41 (1992), p. 147; and in: "Handbook of Incidence Geometry", ed. by F.
Buekenhout, Elsevier Science, Amsterdam, 1995, p. 273; but presumably dating
back to 1965). Our result relies on the classification of the finite
2-transitive permutation groups.Comment: 27 pages; to appear in the journal "Advances in Geometry
New Combinatorial Construction Techniques for Low-Density Parity-Check Codes and Systematic Repeat-Accumulate Codes
This paper presents several new construction techniques for low-density
parity-check (LDPC) and systematic repeat-accumulate (RA) codes. Based on
specific classes of combinatorial designs, the improved code design focuses on
high-rate structured codes with constant column weights 3 and higher. The
proposed codes are efficiently encodable and exhibit good structural
properties. Experimental results on decoding performance with the sum-product
algorithm show that the novel codes offer substantial practical application
potential, for instance, in high-speed applications in magnetic recording and
optical communications channels.Comment: 10 pages; to appear in "IEEE Transactions on Communications
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