The tensor rank of semifields of order 16 and 81

We determine the tensor rank of all semifields of order 16 over F-2 and of all semifields of order 81 over F-3. Our results imply that some semifields of order 81 have lower multiplicative complexity than the finite field F-81 over F-3. We prove new results on the correspondence between linear codes and tensor rank, including a generalisation of a theorem of Brockett and Dobkin to arbitrary tensors, which makes the problem computationally feasible.(C) 2022 Elsevier Inc. All rights reserved.