In this paper we try to shed a new insight on Verifiable Secret Sharing Schemes (VSS). We first define a new "metric" (with slightly different properties than the standard Hamming metric). Using this metric we define a very particular class of codes that we call error-set correcting codes, based on a set of forbidden distances which is a monotone decreasing set. Next we redefine the packing problem for the new settings and generalize the notion of error-correcting capability of the error-set correcting codes accordingly (taking into account the new metric and the new packing). Then we consider burst-error interleaving codes proposing an efficient burst-error correcting technique, which is in fact the well known VSS and Distributed Commitments (DC) pair-wise checking protocol and we prove the error-correcting capability of the error-set correcting interleaving codes.