33.5.1 Remainder Substitution Procedure

The substitute function evaluates the polynomial remainder, with different values of the field primitive elements. The finite field arithmetic addition operation is performed with the Exclusive or. The finite field arithmetic multiplication operation is performed through the gf_log, gf_antilog lookup tables.

The REM2NP1 and REMN2NP3 fields of the PMECC Remainder x registers (PMECC_REMx) contain only odd remainders. Each bit indicates whether the coefficient of the polynomial remainder is set to zero or not.

NB_ERROR_MAX defines the maximum value of the error correcting capability.

NB_ERROR defines the error correcting capability selected at encoding/decoding time.

NB_FIELD_ELEMENTS defines the number of elements in the field.

si[] is a table that holds the current syndrome value, an element of that table belongs to the field. This is also a shared variable for the next step of the decoding operation.

int substitute()
    {
    int i;
    int j;
    for (i = 1; i < 2 * NB_ERROR_MAX;
        i++)
    {
     si[i] = 0;
    }
    for (i = 1; i < 2*NB_ERROR;
        i++)
    {
     for (j = 0; j < oo[i];
      j++)
     {
      if (REM2NPX[i][j])
      {
       si[i] = gf_antilog[(i *
        j)%NB_FIELD_ELEMENTS] ^ si[i];
      }
     }
    }
    return 0;
    }