A magnetic tape device or system can store erasure encoded data that generates a multi-dimensional erasure code corresponding to an erasure encoded object comprising a code-word (CW). The multi-dimensional erasure code enables using a single magnetic tape in response to a random object/file request, and correct for an error within the single magnetic tape without using other tapes. Encoding logic can further utilize other magnetic tapes to generate additional parity tapes that recover data from an error of the single magnetic tape in response to the error satisfying a threshold severity for a reconstruction of the erasure coded object or chunk (s) of the CW. The encoding logic can be controlled, at least in part, by one or more iterative coding processes between multiple erasure code dimensions that are orthogonal to one another
