3.2.19.1 Remainder Substitution Procedure

The substitute function evaluates the remainder polynomial, with different values of the field primitive element. The addition arithmetic operation is performed with the exclusive OR. The multiplication arithmetic operation is performed through the gf_log and gf_antilog lookup tables.

The REM2NP1 and REMN2NP3 fields of the PMECCREMN registers contain only odd remainders. Each bit indicates whether the coefficient of the remainder polynomial 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.

oo[] is a table that contains the degree of the remainders.

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;
}