1. A method for execution by a dispersed storage and task (DST) processing unit that includes a processor, the method comprises: receiving a data object for storage in a distributed storage network (DSN) via a network; generating available storage unit data indicating a subset of a plurality of storage units of the DSN that corresponds to a plurality of available storage units; generating a shortened encoding matrix based on an original encoding matrix and the available storage unit data, wherein a size of the shortened encoding matrix is based on a number of storage units in the plurality of available storage units; and generating a plurality of encoded slices, each for transmission to one of the plurality of available storage units via the network, by performing an encoding function on the shortened encoding matrix and the data object.