Singular Manual: dual_code

| #### D.10.1.11 dual_code Procedure from library `brnoeth.lib` (see brnoeth_lib). Usage: dual_code(G); G a matrix of numbers Return: a generator matrix of the dual code generated by G Note: The input should be a matrix G of numbers. The output is also a parity check matrix for the code defined by G Example:
    LIB "brnoeth.lib";
    ring s=2,T,lp;
    // here is the Hamming code of length 7 and dimension 3
    matrix G[3][7]=1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0,1,1,1,1;
    print(G);
    ==> 1,0,1,0,1,0,1,
    ==> 0,1,1,0,0,1,1,
    ==> 0,0,0,1,1,1,1
    matrix H=dual_code(G);
    print(H);
    ==> 1,1,1,0,0,0,0,
    ==> 1,0,0,1,1,0,0,
    ==> 0,1,0,1,0,1,0,
    ==> 1,1,0,1,0,0,1

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