No.

How come?

AI are normally created from a dead doner's host brain. The brain is destroyed in the process of making a complicated matrix that resembles the host's brain, making all SMART AI similar to their past-living host's brain. EX: Cortana and Halsey, SIF from Contact Harvest containing many Human mannerisms, or even Black Box from the Kilo-5 series. As such, the brain is organic and cannot be perfectly recreated unless [u]cloned[/u] which is banned in the 26th century. Cortana was created from 1 of 3 cloned brains that Doctor Halsey created from her own brain. This makes Cortana unique in a few different ways. 1. Cortana was created from a cloned brain, unless we can get another cloned brain from Dr. Halsey (which is illegal), she wouldn't be the "same Cortana". 2. Cortana was exceptionally smart, picking up on trace things nobody could tell, stemming from being born from Halsey's brain, one of the most if not THE most complex and intelligent minds mankind has ahold of. This probably makes the process a bit tougher if not atleast longer. 3. Not every attempt at creating Cortana was successful, as the Cortana we know was 1 of 3 being created, and the only one to survive the actual process of being created. 4. Dr. Halsey was one of the few who understands how to create a smart AI as she was one of the core scientists who even made smart AI's exist, an example being when she whispers "undid iridium" to Roland aboard the UNSC INFINITY. This causes him to glitch. Roland is a relatively young SMART AI, meaning he should be more sophisticated, however the secret phrase still completely shut him down and rendered him useless. 5. Unless we had a pre-existing piece of Cortana (AI fragment themselves all of the time to complete multiple tasks at once) it would be pretty impossible to recreate Cortana. Furthermore, without an already existing piece of Cortana to integrate, it literally just wouldn't be the same Cortana. It could look and act the same, but wouldn't contain her real memories, like discovering Halo with Chief. 6. Would Halsey even want to create another Cortana? She compared Cortana not only to herself, but to her daughter Miranda, stating they look similar. Cortana was around so Halsey could have someone as smart as herself to discuss and analyze with. The one plausible way I see Cortana coming back is if the UNSC had data of her that was still around from The Mantle's Approach when it attacked Earth, but even this is unplausible. The podium you place Cortana's chip in to disable the UR-Didact's shield gets completely disintegrated, only allowing Cortana to survive in the ship's systems. This doesn't even really make sense to me because we see Chief carrying (what we think) is Cortana's data chip in all of the HALO 5 promotional stuff, but yet it was disintegrated. To be honest, I tried giving you good explanations to the best of my knowledge but LoA will eventually reply and point out some flaws or give you a detailed enough answer. Sorry for the TL;DR lol.

Thanks for the detailed response. [spoiler]I know that, but thanks anyway. =} [/spoiler]

Yeah man all good, I've seen you post here for a while but these forums went to shit ever since Destiny became a thing. I joined here years ago for Halo and it seems some of the only cool members still around are ones interested in Halo. I try not to steal LoA's lightning but I also try to and like keeping the Halo part of these forums alive. Sorry I can't really explain what ya wanna know, I'm interested to see why LoA thinks she can't be recreated since I know alot and still can't give an answer lol