65.61 HammingCode

HammingCode( r, F )

HammingCode returns a Hamming code with redundancy r over F. A Hamming code is a single-error-correcting code. The parity check matrix of a Hamming code has all nonzero vectors of length r in its columns, except for a multiplication factor. The decoding algorithm of the Hamming code (see Decode) makes use of this property.

If q is the size of its field F, the returned Hamming code is a linear
[(q^<r>-1)/(q-1), (q^<r>-1)/(q-1) - <r>, 3] code.

    gap> C1 := HammingCode( 4, GF(2) );
    a linear [15,11,3]1 Hamming (4,2) code over GF(2)
    gap> C2 := HammingCode( 3, GF(9) );
    a linear [91,88,3]1 Hamming (3,9) code over GF(9) 

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