/// <param name="s">Output sequence as polynomial</param>
/// <param name="C">Fills the given polynomial with LFSR Connection Polynomial</param>
/// <returns>Returns the Linear Complexity of given sequence</returns>
public static int BerlekampMassey(Polynomial s, out Polynomial Conn)
{
Polynomial C = new Polynomial(s.Field, 1);
Polynomial B = new Polynomial(s.Field, 1);
int N = s.Degree + 1;
int L = 0;
int m = 1;
FiniteFieldElement b = s.Field.Elements[1];
int n;
for (n = 0; n < N; n++)
{
// calculate discrepency
FiniteFieldElement d = new FiniteFieldElement();
d = s.Coefficients[n];
for (int i = 1; i <= L; i++)
{
try
{
d += C.Coefficients[i] * s.Coefficients[n - i];
}
catch { }
}
if (d.Value == 0)
{
m++;
}
else if (2 * L <= n)
{
Polynomial T = new Polynomial();
T = C;
Polynomial c1 = Polynomial.GenerateFromTerm(s.Field, d * b.Inverse, m);
C = C - (c1 * B);
L = n + 1 - L;
B = T;
b = d;
m = 1;
}
else
{
Polynomial c1 = Polynomial.GenerateFromTerm(s.Field, d * b.Inverse, m);
C = C - (c1 * B);
m++;
}
}
Conn = C;
return(L);
}
/// <returns>Remainder r of polynomials a and b s.t. a = b*q + r</returns>
public static Polynomial operator %(Polynomial a, Polynomial b)
{
if (a.Field.Characteristic != b.Field.Characteristic)
{
throw new Exception("Both polynomials should be defined in the same field.");
}
//if (a.Degree < b.Degree)
//{
// throw new Exception("First polynomial should have higher degree.");
//}
Polynomial result = new Polynomial(a.Field, 0);
Polynomial r = (Polynomial)a.MemberwiseClone(), q = new Polynomial(a.Field, 0);
while (r.Degree >= b.Degree && b.Degree != 0)
{
q = Polynomial.GenerateFromTerm(r.Field, r._coefficients[r._coefficients.Length - 1] / b._coefficients[b._coefficients.Length - 1], r.Degree - b.Degree);
result += q;
r = r - (b * q);
}
return(r);
}