79,056 research outputs found
Characterizing extremal digraphs for identifying codes and extremal cases of Bondy's theorem on induced subsets
An identifying code of a (di)graph is a dominating subset of the
vertices of such that all distinct vertices of have distinct
(in)neighbourhoods within . In this paper, we classify all finite digraphs
which only admit their whole vertex set in any identifying code. We also
classify all such infinite oriented graphs. Furthermore, by relating this
concept to a well known theorem of A. Bondy on set systems we classify the
extremal cases for this theorem
Almost separating and almost secure frameproof codes over q-ary alphabets
The final publication is available at Springer via http://dx.doi.org/10.1007/s10623-015-0060-zIn this paper we discuss some variations of the notion of separating code for alphabets of arbitrary size. We show how the original definition can be relaxed in two different ways, namely almost separating and almost secure frameproof codes, yielding two different concepts. The new definitions enable us to obtain codes of higher rate, at the expense of satisfying the separating property partially. These new definitions become useful when complete separation is only required with high probability, rather than unconditionally. We also show how the codes proposed can be used to improve the rate of existing constructions of families of fingerprinting codes.Peer ReviewedPostprint (author's final draft
Sums of residues on algebraic surfaces and application to coding theory
In this paper, we study residues of differential 2-forms on a smooth
algebraic surface over an arbitrary field and give several statements about
sums of residues. Afterwards, using these results we construct
algebraic-geometric codes which are an extension to surfaces of the well-known
differential codes on curves. We also study some properties of these codes and
extend to them some known properties for codes on curves.Comment: 31 page
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