Dear Stas Bulygin,

You asked:

gap> 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> ]

What should I do to obtain the generator matrix in the explicit form, or how
should I read this output?

There are several ways of doing that, for example:

gap> m:=GeneratorMat(HammingCode(3,GF(2)));;
gap> Display( m );
 1 1 1 . . . .
 1 . . 1 1 . .
 . 1 . 1 . 1 .
 1 1 . 1 . . 1
gap> List( m, x -> List( x, y -> y ) );
[ [ 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 ] ]

I hope this helps.

Best wishes,

Willem de Graaf

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