http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.80....
where the authors explicitly write: "Shamir's scheme for sharing secrets is closely related to Reed-Solomon coding schemes."
now, my eyes glaze over when it comes to the math, so I'll need to look it through a few times before I understand what they are saying.
You can combine the reconstruction properties of Reed Solomon (you need k of n pieces) with the All or Nothing Transform. Encrypting data so that you need all of the data to decrypt.
Then you can essentially do Shamir secret sharing witout storage overhead. A 1 MB file split so you need 5 pieces would have 200 KB pieces instead of 1mb pieces. This is at a cost of exchanging information theoretic security for computational security.