I've found clear explanation of the solution here. Thanks to Justin for this link.
There you can find Python and Java implementations of the algorithm (C++ implementation contains errors).
And here is C# implementation that is just a translation of those algorithms.
public static int LongestPalindrome(string seq)
{
int Longest = 0;
List<int> l = new List<int>();
int i = 0;
int palLen = 0;
int s = 0;
int e = 0;
while (i<seq.Length)
{
if (i > palLen && seq[i-palLen-1] == seq[i])
{
palLen += 2;
i += 1;
continue;
}
l.Add(palLen);
Longest = Math.Max(Longest, palLen);
s = l.Count - 2;
e = s - palLen;
bool found = false;
for (int j = s; j > e; j--)
{
int d = j - e - 1;
if (l[j] == d)
{
palLen = d;
found = true;
break;
}
l.Add(Math.Min(d, l[j]));
}
if (!found)
{
palLen = 1;
i += 1;
}
}
l.Add(palLen);
Longest = Math.Max(Longest, palLen);
return Longest;
}