Reproducing data utilizing a zero information gain function

A dispersed storage (DS) module comprises:

• a first module, when operable within a computing device, causes the computing device to:
• receive a zero information gain (ZIG) encoded data slice and a subset of encoded data slices of a set of encoded data slices, wherein data was encoded using a dispersed storage error coding function to produce the set of encoded data slices, wherein the data can be recreated from a decode threshold number of encoded data slices of the set of encoded data slices, wherein the subset of encoded data slices includes less than the decode threshold number of encoded data slices and does not include a first or a second encoded data slice of the set of encoded data slices, and wherein the ZIG encoded data slice represents a first component of recovery information of the first encoded data slice that is based on the second encoded data slice;
• a second module, when operable within the computing device, causes the computing device to:
• generate a set of ZIG encoded data slices using a ZIG function and corresponding ones of the subset of encoded data slices, wherein the set of ZIG encoded data slices represents additional components of the recovery information of the first encoded data slice;
• a third module, when operable within the computing device, causes the computing device to:
• recreate the first encoded data slice from the ZIG encoded data slice and the set of ZIG encoded data slices;
• and
• a fourth module, when operable within the computing device, causes the computing device to:
• decode the subset of encoded data slices and the first encoded data slice using the dispersed storage error coding function to reproduce the data.