Almost-perfect secret sharing

To split a secret s between several participants, we generate (for each value of s) shares for all participants. The goal: authorized groups of participants should be able to reconstruct the secret but forbidden ones get no information about it. We introduce several notions of non-perfect secret sharing, where some small information leak is permitted. We study its relation to the Kolmogorov complexity version of secret sharing (establishing some connection in both directions) and the effects of changing the secret size (showing that we can decrease the size of the secret and the information leak at the same time).