Singular Manual: syndrome

| #### D.10.2.6 syndrome Procedure from library `decodegb.lib` (see decodegb_lib). Usage: syndrome (h, c); h a check matrix, c a row vector (codeword) Return: corresponding syndrome Example:
    LIB "decodegb.lib";
    ring r=2,x,dp;
    matrix x[1][4]=1,0,1,0;
    matrix g[4][7]=1,0,0,0,0,1,1,
    0,1,0,0,1,0,1,
    0,0,1,0,1,1,1,
    0,0,0,1,1,1,0;
    //encode x with the generator matrix g
    matrix c=encode(x,g);
    // disturb
    c[1,3]=0;
    //compute syndrome
    //corresponding check matrix
    matrix check[3][7]=1,0,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,1;
    print(syndrome(check,c));
    ==> 0,
    ==> 0,
    ==> 1
    c[1,3]=1;
    //now c is a codeword
    print(syndrome(check,c));
    ==> 0,
    ==> 0,
    ==> 0

User manual for Singular version 4.4.1, 2025, generated by texi2html.