65.123 GrayMat

GrayMat( n, F )

GrayMat returns a list of all different vectors (see Vectors) of length n over the field F, using Gray ordening. n must be a positive integer. This order has the property that subsequent vectors differ in exactly one coordinate. The first vector is always the null vector. Each call to GrayMat returns a new matrix, so it is safe to modify the result.

    gap> GrayMat(3);
    [ [ 0*Z(2), 0*Z(2), 0*Z(2) ], [ 0*Z(2), 0*Z(2), Z(2)^0 ],
      [ 0*Z(2), Z(2)^0, Z(2)^0 ], [ 0*Z(2), Z(2)^0, 0*Z(2) ],
      [ Z(2)^0, Z(2)^0, 0*Z(2) ], [ Z(2)^0, Z(2)^0, Z(2)^0 ],
      [ Z(2)^0, 0*Z(2), Z(2)^0 ], [ Z(2)^0, 0*Z(2), 0*Z(2) ] ]
    gap> G := GrayMat( 4, GF(4) );; Length(G);
    256          # the length of a GrayMat is always $q^n$
    gap> G[101] - G[100];
    [ 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ] 

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