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I am reading about an algorithm for finding minimum-weight words in large linear codes. Let $c$ be the codeword of weight $w$ to recover (with size $n$ and in $GF(2)$). Let $N = \left\{1, 2, \ldots, n\right\}$ and $I\subset N$ ($|I| = k$). Let $\left\{X_i\right\}_{i\in N}$ be a stochastic process which corresponds to the number of nonzero bits of $c$ in $I$ and the random variable $X_i$ take its values in the set $\left\{1, 2, \ldots, w\right\}$. The state space of the stochastic process is:

$$E = \left\{1, \cdots, 2p - 1\right\} \cup \left\{2p\right\} \cup \left\{2p + 1, \cdots, w\right\}$$

where

$X_i = u$ iff $|I\cap \textrm{supp}(c)| = u$, $\forall u \in \left\{1, \cdots, 2p-1\right\} \cup \left\{2p + 1, \cdots, w\right\}.$

My questions are: Why the initial probabilty vector is $\pi_0(u)=\dfrac{C^{w}_u C^{n-w}_{k-u}}{C^{n}_k}$, if $u \notin \left\{{2p}\right\}$. And the most important: How to interpret these combinatorials?.

Definition: $\textrm{supp}(c)$ is a set with coordinates of nonzero bits in $c$.

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    a) What does "pdta" mean? Is there a reason you let us guess an abbreviation instead of pressing a few more keys to write it out? b) Your definition of $\operatorname{supp}$ as a number in the last line is inconsistent with its use as a set further up. c) What's $p$? What's the significance of $2p$ being singled out in $E$ and removed from the options for $u$?2012-12-12
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    @joriki thanks by your feedback, I edit a question.2012-12-12
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    You haven't resolved the discrepancy between the definition of $\operatorname{supp}$ as a number and its use as a set. Also the addition of $u\notin\{2p\}$ hasn't clarified the role of $p$ for me.2012-12-12
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    $2p$ haven't relevance2012-12-13
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    Yes haven't relevance, please members help me with this question,2012-12-27

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