In coding theory, there are parity-check codes whose parity-check matrices H are generated via column permutations. For instance, the LDPC codes constructed in Gallager's 1962 IRE Trans paper uses the following H matrix:

[ X1 ]

[ X2 ]

[ .... ]

[ Xn ]

where submatrices X2 .. Xn are just random column permutations of X1. However, to make the codes efficient in decoding, there is one restriction which requires that any two row vectors in...

Dear All,

I'm a beginner who is learning Finite Field under the help of Maple. I'm wondering is there a command to compute the minimal polynomials for the members of a finite field?

For instance, for GF(16) realized by the polynomial a^4 = a + 1,we know that for a's minimal polynomial is x^4 + x + 1, a^3's minimal polynomial is x^4 + x^3 + x^2 + x + 1. In Maple, how do I reproduce such result?

Thank you very much for your help,

Best,

Kelvin