Singular Manual: genMDSMat

  | #### D.10.2.11 genMDSMat Procedure from library `decodegb.lib` (see decodegb_lib). Usage: genMDSMat(n, a); n is int, a is number
              - n x n are dimensions of the MDS matrix,
              - a is a primitive element of the field.
Note: An MDS matrix is constructed in the following way. We take 'a' to be a generator of the multiplicative group of the field. Then we construct the Vandermonde matrix with this 'a'. Assume: extension field should already be defined Return: a matrix with the MDS property. Example:
    LIB "decodegb.lib";
    int q=16; int n=15;
    ring r=(q,a),x,dp;
    //generate an MDS (Vandermonde) matrix
    matrix h_full=genMDSMat(n,a);
    print(h_full);
    ==> 1,1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,
    ==> 1,a,  a2, a3, a4, a5, a6, a7, a8, a9, a10,a11,a12,a13,a14,
    ==> 1,a2, a4, a6, a8, a10,a12,a14,a,  a3, a5, a7, a9, a11,a13,
    ==> 1,a3, a6, a9, a12,1,  a3, a6, a9, a12,1,  a3, a6, a9, a12,
    ==> 1,a4, a8, a12,a,  a5, a9, a13,a2, a6, a10,a14,a3, a7, a11,
    ==> 1,a5, a10,1,  a5, a10,1,  a5, a10,1,  a5, a10,1,  a5, a10,
    ==> 1,a6, a12,a3, a9, 1,  a6, a12,a3, a9, 1,  a6, a12,a3, a9,
    ==> 1,a7, a14,a6, a13,a5, a12,a4, a11,a3, a10,a2, a9, a,  a8,
    ==> 1,a8, a,  a9, a2, a10,a3, a11,a4, a12,a5, a13,a6, a14,a7,
    ==> 1,a9, a3, a12,a6, 1,  a9, a3, a12,a6, 1,  a9, a3, a12,a6,
    ==> 1,a10,a5, 1,  a10,a5, 1,  a10,a5, 1,  a10,a5, 1,  a10,a5,
    ==> 1,a11,a7, a3, a14,a10,a6, a2, a13,a9, a5, a,  a12,a8, a4,
    ==> 1,a12,a9, a6, a3, 1,  a12,a9, a6, a3, 1,  a12,a9, a6, a3,
    ==> 1,a13,a11,a9, a7, a5, a3, a,  a14,a12,a10,a8, a6, a4, a2,
    ==> 1,a14,a13,a12,a11,a10,a9, a8, a7, a6, a5, a4, a3, a2, a
See also: Decoding method based on quadratic equations.

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