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These are replies submitted by Magma

@Carl Love You right. I made a mistake. Thank you. 

@vv I appreciate you taking the time to respond to my comment. Your solution is nice and perfect and not only is useful for this question, but also can be used for other commands of generic package.

I would like to ask you to help me in the next question which is the my last question. I attached a new maple file. In the new Maple file, there is an 8x16 matrix over GF(2,4)  which is denoted with  H. I used the matrix H as a parity-check matrix of a code and observe that H produces the [16,8,7] code which means the minimum number of linearly dependent columns of H over G is 7. But when I test the matrix H with your given solution I got 8 for the rank of matrix. Where is my mistake. In other words, how to obtain the minimum number of linearly dependent columns of H with your given solution.

Excuse me that I ask too questions. I am a TA of coding and I would like to implement the concept of coding with Maple.

@vv Thanks for your answer.I tested your suggestion, but the ReducedRowEchelon  command makes an error when the matrix is not a square matrix.I attached the Maple file to see the example. As you know, my question is equivalent to obtain the minimum distance of a code when the matrix H is used as a parity-check matrix in the code. Thanks

@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.

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