Dear GAP-Forum,

gap> RequirePackage("guava");
gap> G:=GeneratorMat(HammingCode(3,GF(2)));
[ <an immutable GF2 vector of length 7>, <an immutable GF2 vector of
length 7>
    , <an immutable GF2 vector of length 7>,
  <an immutable GF2 vector of length 7> ]
gap> GM:=[];
[  ]
gap> for j in [1..4] do
> GM[j]:=List([1..7],i->G[j][i]);
> od;
gap> GM;
[ [ Z(2)^0, Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ],
  [ Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2) ],
  [ 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2) ],
  [ Z(2)^0, Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0 ] ]

The object G here *is* the 4 by 7 matrix over GF(2) you are looking for. It
is just that it is printed in a slightly strange way (more precisely, the
"View" method is a bit strange, we can think about changing this in upcoming
versions of GAP).

You can use one of the following commands to look at the object G directly:

gap> G:=GeneratorMat(HammingCode(3,GF(2)));
[ <an immutable GF2 vector of length 7>, <an immutable GF2 vector of length 7>
    , <an immutable GF2 vector of length 7>,
  <an immutable GF2 vector of length 7> ]
gap> Display(G);
 1 1 1 . . . .
 1 . . 1 1 . .
 . 1 . 1 . 1 .
 1 1 . 1 . . 1
gap> Print(G);
[ [ Z(2)^0, Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ],
  [ Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2) ],
  [ 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2) ],
  [ Z(2)^0, Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0 ] ]gap>

With best regards,

Frank Lübeck

///  Dr. Frank Lübeck, Lehrstuhl D für Mathematik, Templergraben 64,  ///
\\\                    52062 Aachen, Germany                          \\\
///  E-mail: Frank.Luebeck@Math.RWTH-Aachen.De                        ///
\\\  WWW:    http://www.math.rwth-aachen.de/~Frank.Luebeck/           \\\