65.43 Decode

Decode( C, c )

Decode decodes c with respect to code C. c is a codeword or a list of codewords. First, possible errors in c are corrected, then the codeword is decoded to an information codeword x. If the code record has a field specialDecoder, this special algorithm is used to decode the vector. Hamming codes and BCH codes have such a special algorithm. Otherwise, syndrome decoding is used. Encoding is done by multiplying the information vector with the code (see Operations for Codes).

A special decoder can be created by defining a function

C.specialDecoder := function(C, c) ... end;

The function uses the arguments C, the code record itself, and c, a vector of the codeword type, to decode c to an information word. A normal decoder would take a codeword c of the same word length and field as C, and would return a information word of length k, the dimension of C. The user is not restricted to these normal demands though, and can for instance define a decoder for non-linear codes.

    gap> C := HammingCode(3);
    a linear [7,4,3]1 Hamming (3,2) code over GF(2)
    gap> c := "1010"*C;                    # encoding
    [ 1 0 1 0 1 0 1 ]
    gap> Decode(C, c);                     # decoding
    [ 1 0 1 0 ]
    gap> Decode(C, Codeword("0010101"));
    [ 1 0 1 0 ]                            # one error corrected
    gap> C.specialDecoder := function(C, c)
    > return NullWord(Dimension(C));
    > end;
    function ( C, c ) ... end
    gap> Decode(C, c);
    [ 0 0 0 0 ]           # new decoder always returns null word 

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