# Markov Chain + Decoding algorithm

I am ready a paper Canteaut and Chabaud, I don't get understand the values of transition matrix $P$, in the Proposition 4. If, anybody read this paper please help me understand this values: $P_{u,u}$, $P_{u,u-1}$, etc.

-

$P_{u,v}$ is the probability of a transition between state $u$ to state $v$. It's described more formally in Definition 3 where for a given Markov chain $X$, the conditional probability $P(X_i = v | X_{i-1} = u) = P_{u,v}$.
thanks by your response, but is just this that I don't uderstand for example Why $$P_{u,u}=\dfrac{k-u}{k}\times \dfrac{n-k-(w-u)}{n-k}+\dfrac{u}{k}\times \dfrac{w-u}{n-k}$$ – juaninf Dec 11 '12 at 0:10