65.44 Syndrome

Syndrome( C, c )

Syndrome returns the syndrome of word c with respect to a code C. c is a word of the vector space of C. If c is an element of C, the syndrome is a zero vector. The syndrome can be used for looking up an error vector in the syndrome table (see SyndromeTable) that is needed to correct an error in c.

A syndrome is not defined for non-linear codes. Syndrome then returns an error.

    gap> C := HammingCode(4);
    a linear [15,11,3]1 Hamming (4,2) code over GF(2)
    gap> v := CodewordNr( C, 7 );
    [ 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 ]
    gap> Syndrome( C, v );
    [ 0 0 0 0 ]
    gap> Syndrome( C, "000000001100111" );
    [ 1 1 1 1 ]
    gap> Syndrome( C, "000000000000001" );
    [ 1 1 1 1 ]    # the same syndrome\: both codewords are in the same
                   # coset of C 

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