According to the FAQ it uses a Shamir Secret Sharing Scheme to split an encryption key. But you can actually use a Reed-Solomon scheme[1] and have no encryption key to achieve this objective.
First, you process the input data with an all-or-nothing transform (AONT)[2]. Then you split it into Reed-Solomon shares. AONT is required due to Reed-Solomon being vulnerable to a distinguisher[3] and it will most likely leak information about its input.
Is that approach information-theoretically secure? Shamir Secret Sharing is, and the mathematics is very simple.
Note that the encryption step is, strictly speaking, not necessary for Shamir either. But there are benefits to encrypting the secret and only using SSS for the key (I'm not sure if that's how Horcrux works, but that's how my fairly-similar tool Paperback[1] works).
First, you process the input data with an all-or-nothing transform (AONT)[2]. Then you split it into Reed-Solomon shares. AONT is required due to Reed-Solomon being vulnerable to a distinguisher[3] and it will most likely leak information about its input.
[1] <https://en.wikipedia.org/wiki/Reed%E2%80%93Solomon_error_cor...>
[2] <https://en.wikipedia.org/wiki/All-or-nothing_transform>
[3] <https://en.wikipedia.org/wiki/Distinguishing_attack>