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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