  The problem of straggler mitigation in distributed matrix multiplication
(DMM) is considered for a large number of worker nodes and a fixed small finite
field. Polynomial codes and matdot codes are generalized by making use of
algebraic function fields (i.e., algebraic functions over an algebraic curve)
over a finite field. The construction of optimal solutions is translated to a
combinatorial problem on the Weierstrass semigroups of the corresponding
algebraic curves. Optimal or almost optimal solutions are provided. These have
the same computational complexity per worker as classical polynomial and matdot
codes, and their recovery thresholds are almost optimal in the asymptotic
regime (growing number of workers and a fixed finite field).
