guava - Gap

GUAVA 30
[ 1 1 ]
gap> m*C;
[ 1 1 0 0 ]
4.2.4 InformationWord
♦ InformationWord(C, c)
(function)
Here C is a linear code and c is a codeword in it. The command InformationWord returns
the message word (or ’information digits’) m satisfying c=m*C. This command simply calls Decode,
provided c in C is true. Otherwise, it returns an error.
To invert this, use the encoding function * (see * (4.2.3)).
Example
gap> C:=HammingCode(3);
a linear [7,4,3]1 Hamming (3,2) code over GF(2)
gap> c:=Random(C);
[ 0 0 0 1 1 1 1 ]
gap> InformationWord(C,c);
[ 0 1 1 1 ]
gap> c:=Codeword("1111100");
[ 1 1 1 1 1 0 0 ]
gap> InformationWord(C,c);
"ERROR: codeword must belong to code"
gap> C:=NordstromRobinsonCode();
a (16,256,6)4 Nordstrom-Robinson code over GF(2)
gap> c:=Random(C);
[ 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 1 ]
gap> InformationWord(C,c);
"ERROR: code must be linear"
4.3 Boolean Functions for Codes
4.3.1 in
♦ in(c, C)
(function)
The command c in C evaluates to ‘true’ if C contains the codeword or list of codewords specified
by c. Of course, c and C must have the same word lengths and base fields.
Example
gap> C:= HammingCode( 2 );; eC:= AsSSortedList( C );
[ [ 0 0 0 ], [ 1 1 1 ] ]
gap> eC[2] in C;
true
gap> [ 0 ] in C;
false