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le (8m33s)

## 3.8. Becker, Joux, May, and Meurer Algorithm

Now in session 8, we will present yet another evolution of information set decoding. Before presenting this improvement, we will first improve the Birthday Decoding algorithm what I call a Further Improvement of Birthday Decoding. I will consider the two following lists. The difference between those two lists and those we had before is the + ɛ that you can find in the weight of the errors e1 and e2. Those lists depend on another parameter ɛ. What is the meaning of that parameter? Well, the idea is the following: if ...
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le (8m30s)

## 5.6. The diversity of bioinformatics algorithms

In this course, we have seen a very little set of bioinformatic algorithms. There exist numerous various algorithms in bioinformatics which deal with a large span of classes of problems. For example, read assembly. We have seen how NGS sequencers produce large sets of reads, small sequences which overlap. And the problem of assembly isto use the overlap in order to ordering this read and reconstructing the whole genomic sequence. This is the overlapping and you see that you can use this overlap to get a longer sequence. Of course, here the example issimple: you have to imagine a set of millions of reads to beassembled into genomic sequences of millions or ...
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le (8m27s)

## 3.9. Generalized Birthday Algorithm for Decoding

The session nine is devoted to the application of the Generalized Birthday Algorithm to decoding. The Generalized Birthday Algorithm was presented by David Wagner in 2002, in a more general context. In fact, at order a, the Generalized Birthday Algorithm solves the following problem: we are given 2^a lists of vectors of size L and we want to find xi, one in every list Li, such that the sum of all the xi is 0. If the lists Li are large enough, then the algorithm runs in time 2^(l/(a+1)). Note that the ...
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