How to create a Markov chain sequence given the transition matrix and the states

There is 5 states as follows:

QS=[2.0243
   -0.6361
    0.7770
    1.0486
    1.1569]   % or QS={2.024 ,-0.6361 ,0.7770,  1.0486 ,1.1569}

And this is the transition matrix that has the probabilities of going from one state to another:

   P=[0.5000    0.0556    0.0556    0.0556    0.0556
      0.0556    0.5000    0.0556    0.0556    0.0556
      0.0556    0.0556    0.5000    0.0556    0.0556
      0.0556    0.0556    0.0556    0.5000    0.0556
      0.0556    0.0556    0.0556    0.0556    0.5000];

How can I get a Markov chain sequence Js=[Js(1)...Js(t)] from these given P and QS? (t is a given time)

I used the following code to produce the sequence but it does not use the state space which is known in computing the sequence.

          transition_probabilities=P;
          chain_length=512;
            chain = zeros(1,chain_length);      
                chain(1)=starting_value;   %Starting value=1;
                for i=2:chain_length
                     this_step_distribution = transition_probabilities(chain(i-1),:);
                     cumulative_distribution = cumsum(this_step_distribution);
                     r = rand();
                     chain(i) = find(cumulative_distribution>r,1);
                 end

Will I still get the right sequence, even if I don't use the State space?

[shahab anjum]

can u please tell me how u get the transition probablity matrix please