/// <summary>
/// Encode a number between 0 and (n|t) (binomial coefficient) into a binary vector of length n with weight t.
/// <para>The number is given as a byte array. Only the first s bits are used, where s = floor[log(n|t)].</para>
/// </summary>
///
/// <param name="N">The "n" integer</param>
/// <param name="T">The "t" integer</param>
/// <param name="M">The message as a byte array</param>
///
/// <returns>The encoded message as GF2Vector</returns>
public static GF2Vector Encode(int N, int T, byte[] M)
{
if (N < T)
{
throw new ArgumentException("n < t");
}
// compute the binomial c = (n|t)
BigInteger c = BigMath.Binomial(N, T);
// get the number encoded in m
BigInteger i = new BigInteger(1, M);
// compare
if (i.CompareTo(c) >= 0)
{
throw new ArgumentException("Encoded number too large.");
}
GF2Vector result = new GF2Vector(N);
int nn = N;
int tt = T;
for (int j = 0; j < N; j++)
{
c = c.Multiply(BigInteger.ValueOf(nn - tt)).Divide(BigInteger.ValueOf(nn));
nn--;
if (c.CompareTo(i) <= 0)
{
result.SetBit(j);
i = i.Subtract(c);
tt--;
if (nn == tt)
{
c = ONE;
}
else
{
c = (c.Multiply(BigInteger.ValueOf(tt + 1))).Divide(BigInteger.ValueOf(nn - tt));
}
}
}
return(result);
}
