@Carl Love I appreciate you taking the time to answer my questions.

@vv You right. I dont know why I just searched "random permutation". Thanks for your notation and sorry for my stupid search.

@vv The result for random permutation in my Maple 15 is provided in the following picture 

@Carl Love It's a good suggestion and I wait for it.

@Carl Love I appreciate you for your cooperation in the question. 

@sand15 Thanks for your edition. Your code makes an error that I made a picture to see it. Thanks for your cooperation in the question.

@Kitonum Nice and simple solution. One question: do you suggest that I use the command randomize() in the procedure or in the out of the procedure? Dose it have difference in the results? Thanks 

@Carl Love 

Your command works, but the output in my Maple 15 is different form your solution and is in the following form (I run it several times)

[386408307450,996417214180,412286285840,842622684442,427552056869,800187484459,22424170465,193139816415,395718860534]

@sand15 The command rand(0.0 .. 1.0) does not work in my Maple 15. Is there a type of package for computing this command or maybe is not supported in Maple 15? Thanks for your notation.

@Carl Love You know, I am a beginner user in this site. I asked several questions and I received interesting and nice answers, as you done for me. Today I decided to answer one question that I thought I could help to other user. I accept that your code is efficient  than my code and because of this I appreciate you. I personally respect for your Maple Knowledge. 

@Carl Love Maybe you are right, but your comment is not polite. 

@vv 

Thank you for useful notes that you mentioned. 
As you know, in Table 7 in the following paper 

https://eprint.iacr.org/2016/119.pdf

it is mentioned that the number s for the polynomial f:=x^8+x^4+x^3+x^2+1 is equal to 8+3 and is not possible to find s=10. 

The general problem is that if the polynomial f is an irreducible polynomial of degree n over GF(2), what is the minimum number of s (An nxn binary non-singular matrix with the minimum number of 1's such that its characteristic polynomial is f over GF(2))

Thanks again

@dharr What a nice strategy you did. Really I appreciate you taking the time to get this interesting method.

@dharr 

Thank you for participating in this discussion. Yesterday I asked this question from one of the Prof. of mathematics and today I received his answer. He wrote that this problem is solved for polynomials of degree one to eight in the following paper (Tables 3 to 7)

https://eprint.iacr.org/2016/119.pdf

And it is extended in the next paper 

https://eprint.iacr.org/2019/012.pdf

Thanks again

@vv Thanks for useful note that you mentioned. For me is a strange math problem. We have two irreducible polynomials with the same number of terms ( five terms). for the first one we obtained some solutions and for the second one it seems we could not get  no solutions.