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

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