Q:

What magic can decipher Linguist ciphers?

As part of the Linguist feat, you can write ciphers which are particularly difficult to crack, though the feat indicates that you can use either an Int check or magic to decipher it. For mid-level characters, the DC for the Int check can easily be well over 20, so magic might be a preferable route.
Are there any spells that specifically do this? Comprehend Languages isn't acceptable for a litany of reasons including it's low spell level, the fact that you get only the literal reading, and its specific exception for secret messages. However, nothing else in the PHB seems to fit the bill short of busting out a Wish or capturing the character and reading their mind.
Does this fall into the realm of needing to craft a specific spell?

A:

Nothing is explicitly called out in spell descriptions to allow this, whereas you might get some information with Comprehend Languages on a simple substitution cypher (A= 1, B = 2... ) (DM's purview on that). It might not give all of the information to you. Cyphers are done with a key or primer so your best bet is to cast other divinations, Commune, Locate Object/Person in order to find the scrap of paper or the person that has the primer or key for that cypher.
This of course will not allow you to translate code talking, like 30's film noir did in their spy movies. Or what they do in military transmissions. The turtle is breaking the stream, may not mean anything but to the other side (who has the primer) knows that the tank has crossed the small river and by association of context set up prior knows which river.
And as history showed you can't simply have one level of encryption and expect to remain safe.
As UrhoKarila indicates ciphers and codes are different and any decent spy or underhanded individual would use both in any communique. And since I don't even allow Thieves' Cant as an actual language (because it is not and simply code) CL doesn't work on it in my campaigns.
Inspirational context here, one of my top 5 favorite episodes sort of goes into this Star Trek: The Next Generation Season 5 Episode 2 "Darmok". Excellent case study on this very thing.
Also, another great example (and I will be dating myself a bit here) but Airplane (1980) "Excuse me, I speak Jive..."
I would caution you against making a Golden Hammer spell to crack any code as it would render such abilities and intrigues totally moot.

A:

The only logical method would be magic or knowledge domain clerics, but as Slagmoth points out I would caution against any spell that can decode messages as this will ruin almost all intrique. At the very least should require some divination as into the writer and/or recipient of the message.
The best recommendation I would suggest is find a Knowledge Cleric with Visions of the Past to do a reading on the object (message) to find its owner history, track down and interrogate each of the owners further with detect thoughts. It's quite a high level ability, but role-play may dictate that you could find a cleric of sufficient caliber. On top of that it provides great role-play opportunities.
The reason why I would discourage a single spell covering this is mainly because
long messages can literally have an endless realm possibile of simultaneous meanings that will make sense to someone and each person may come to a different conclusion about the meaning of an encoded message. It does not make sense and even in the realm of magic its hard to extrapolate a spell that would know which one of these thousands of possible meanings was the intended encoding method used by the writer and recipient, especially Comprehend Languages.

