  The weight distribution of a linear code C is put in an explicit bijective
correspondence with Duursma's reduced polynomial of C. We prove that the
Riemann Hypothesis Analogue for a linear code C requires the formal
self-duality of C and imposes an upper bound on the cardinality q of the basic
field, depending on the dimension and the minimum distance of C.
  Duursma's reduced polynomial of the function field of a curve X of genus g
over the field with q elements is shown to provide a generating function for
the numbers of the effective divisors of non-negative degree degree of a
virtual function field of a curve of genus g-1 over the same finite field.
