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These are replies submitted by Magma

@vv Yes the use of floats should be enough. A million thanks to you.

@vv First of all, I want to thank you because of two useful notes that you mentioned. I have two questions.

First: what did you mean by "provided that the entries of C are < 2^53". Do you mean C[i,j]<2^53 for all i and j? 

Second: Consider we defined the finite field G:=GF(2,n) for some n and we considered the matrix A over G by A:=G:-input~(A). Now the computation are done over  GF(2) and hence when by generic package we obtain C=A^k, then all even numbers in C are changed to zero and this is not acceptable. In fact we want to find the primitive order of matrix A over field of real numbers. 

Thanks in advance


@mmcdara Thanks  for your cooperation in the question. 

@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)


@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. 


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

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

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