Encoding data utilizing a zero information gain function

A method for execution by a computing device of a dispersed storage network (DSN), the method comprises:

• dispersed storage error encoding, by the computing device, a data segment of data in accordance with dispersed data storage parameters to produce a set of encoded data slices, wherein the dispersed data storage parameters include a decode threshold number, and wherein the decode threshold number of encoded data slices of the set of encoded data slices is required to recover the data segment;
• selecting, by the computing device, a subset of encoded data slices from the set of encoded data slices, wherein a number of encoded data slices included the subset of encoded data slices is less than the decode threshold number;
• generating, by the computing device, a subset of zero information gain (ZIG) encoded data slices, wherein a first ZIG encoded data slice of the subset of ZIG encoded data slices is generated by matrix multiplying a first decoding matrix and a first encoded data slice of the set of encoded data slices, wherein the first encoded data slice is not included in the subset of encoded data slices, and wherein the data segment is able to be reproduced utilizing the subset of encoded data slices and the subset of ZIG encoded data slices;
• sending, by the computing device, the subset of encoded data slices to a first memory of the DSN for storage therein;
• and
• sending, by the computing device, the subset of ZIG encoded data slices to a second memory of the DSN for storage therein.