Declare a dictionary inside a static class

If you want to declare the dictionary once and never change it then declare it as readonly:

private static readonly Dictionary<string, string> ErrorCodes
    = new Dictionary<string, string>
{
    { "1", "Error One" },
    { "2", "Error Two" }
};

If you want to dictionary items to be readonly (not just the reference but also the items in the collection) then you will have to create a readonly dictionary class that implements IDictionary.

Check out ReadOnlyCollection for reference.

BTW const can only be used when declaring scalar values inline.