65.25 CheckMat

CheckMat( C )

CheckMat returns a parity check matrix of C. The code consists of all words orthogonal to each of the rows of this matrix. The transpose of the matrix is a right inverse of the generator matrix. The parity check matrix is computed from either the generator matrix, the generator polynomial, the check polynomial or the elements of C (if possible), whichever is available.

If C is a non-linear code, the function returns an error.

    gap> CheckMat( HammingCode(3, GF(2) ) );
    [ [ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0 ],
      [ 0*Z(2), Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0 ],
      [ Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0 ] ]
    gap> CheckMat( RepetitionCode( 5, GF(25) ) );
    [ [ Z(5)^0, Z(5)^2, 0*Z(5), 0*Z(5), 0*Z(5) ],
      [ 0*Z(5), Z(5)^0, Z(5)^2, 0*Z(5), 0*Z(5) ],
      [ 0*Z(5), 0*Z(5), Z(5)^0, Z(5)^2, 0*Z(5) ],
      [ 0*Z(5), 0*Z(5), 0*Z(5), Z(5)^0, Z(5)^2 ] ]
    gap> CheckMat( WholeSpaceCode( 12, GF(4) ) );
    [  ] 

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