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The famous max-flow min-cut theorem states that a source node s can send information through a network (V, E) to a sink node t at a rate determined by the min-cut separating s and t. Recently, it has been shown that this rate can also be achieved for multicasting to several sinks provided that the intermediate nodes are allowed to re-encode the information(More)
1 Abstract If C is a q-ary code of length n and a and b are two codewords, then c is called a descendant of a and b if c i 2 fa i ; b i g for i = 1; : : : ; n. We are interested in codes C with the property that, given any descendant c, one can always identify at least one of thèparent' codewords in C. We study bounds on F (n; q), the maximal cardinality of(More)
The famous max-flow min-cut theorem states that a source node <i>s</i> can send information through a network (<i>V,E</i>) to a sink node <i>t</i> at a data rate determined by the min-cut separating <i>s</i> and <i>t</i>. Recently it has been shown that this rate can also be achieved for multicasting to several sinks provided that the intermediate nodes are(More)
A generic (r, m)-erasure correcting set generates for each binary linear code of codimension r a collection of parity check equations that enables iterative decoding of all potentially correctable erasure patterns of size at most m. As we have shown earlier, such a set essentially is just a parity check collection with this property for the Hamming code of(More)
Recently there has been interest in the construction of small parity-check sets for iterative decoding of the Hamming code with the property that each uncorrectable (or stopping) set of size three is the support of a codeword and hence uncorrectable anyway. Here we reformulate and generalize the problem and improve on this construction. We show that a(More)
We consider codes over the alphabet Q = {0, 1,. .. , q − 1} intended for the control of unidirectional errors of level ℓ. That is, the transmission channel is such that the received word cannot contain both a component larger than the transmitted one and a component smaller than the transmitted one. Moreover, the absolute value of the difference between a(More)
A recent publication introduced a Visual Crypto (VC) system, based on the polarisation of light. This VC system has good resolution, contrast and colour properties. Mathematically, the VC system is described by the XOR operation (modulo two addition). In this paper we investigate Threshold Visual Secret Sharing schemes associated to XOR-based VC systems.(More)
We report on block-coding techniques for partial-response II. PRELIMINARY channels with transfer function (1 F Dm), m = 1,2,. . We consider various constructions of block codes with prescribed minimum Euclidean Let u = (x1,... ,un) andv = (VI,..., un) be two n-tuples over distance. Upper and lower bounds to the size of a code with minimum squared Euclidean(More)
A generic (r,m)-erasure correcting set is a collection of vectors in F<sub>2</sub> <sup>r</sup> which can be used to generate, for each binary linear code of codimension r, a collection of parity check equations that enables iterative decoding of all correctable erasure patterns of size at most m. That is to say, the only stopping sets of size at most m for(More)