Bicircular matroids representable over GF(4)GF(4) or GF(5)GF(5)

Given a bicircular matroid B(G)B(G) and q∈{4,5}q∈{4,5}, we characterize when the bicircular matroid B(G)B(G) is GF(q)GF(q)-representable by precisely describing the structure of GG. These descriptions yield polynomial-time algorithms with input GG to certify if B(G)B(G) is or is not GF(q)GF(q)-representable.