The remains of the bird were found in a chimney in Surrey and experts at the intelligence agency GCHQ have been struggling to decipher the message since they were provided with it a few weeks ago.
The agency said it may be impossible to decode it without more information - some of which could come from the public, the 'BBC News' reported.
The message was discovered by David Martin while renovating the chimney of his house. He found parts of a dead pigeon including a leg to which a red canister was attached.
Inside the canister was a thin piece of paper with the words "Pigeon Service" at the top and 27 handwritten blocks of code.
Two pigeon identifying numbers were written on the message with the bird given to GCHQ at the start of the month.
"We didn't really hold out any hopes we would be able to read the message because the sort of codes that were constructed to be used during operations were designed only to be able to be read by the senders and the recipients," said GCHQ historian Tony.
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"Unless you get rather more idea than we have of who actually sent this message and who it was sent to we are not going to find out what the underlying code being used was," he said.
Experts believe there are two ways the message might have been coded - one is with a so-called one-time pad where a random "key" is applied to a message. If the key is truly random and known only to sender and recipient, the code can be unbreakable.
Another option is that this code was based on a specific - and now probably destroyed - code-book put together for a particular operation so the maximum amount of information about that operation could be relayed in the shortest message.