  To multiply astronomic matrices using parallel workers subject to straggling,
we recommend interleaving checksums with some fast matrix multiplication
algorithms. Nesting the parity-checked algorithms, we weave a product code
flavor protection.
  Two demonstrative configurations are as follows: (A) $9$ workers multiply two
$2\times 2$ matrices; each worker multiplies two linear combinations of entries
therein. Then the entry products sent from any $8$ workers suffice to assemble
the matrix product. (B) $754$ workers multiply two $9\times 9$ matrices. With
empirical frequency $99.8\%$, $729$ workers suffice, wherein $729$ is the
complexity of the schoolbook algorithm.
  In general, we propose probability-wisely favorable configurations whose
numbers of workers are close to, if not less than, the thresholds of other
codes (e.g., entangled polynomial code and PolyDot code). Our proposed scheme
applies recursively, respects worker locality, incurs moderate pre- and
post-processes, and extends over small finite fields.
