Blakley type secret sharing scheme based on the intersection of subspaces

We consider the problem of constructing a secret sharing schemes permitting to replace any subset of participants with new participants so that new secret shares may be calculated only for the newly added members, and secret shares of others participants do not change. Using the theory of error-correcting codes we construct protocols of separation and recovery of the secret. In order to study the permissible domains of parameters of this secret sharing scheme the new characteristics of linear code is introduced and explored. We implement the proposed scheme for some linear codes as examples.