A counterexample to 'Algebraic function fields with small class number'

Using class field theory I give an example of a function field of genus 4 with class number one over the finite field F 2 . In a previous paper (see [2, Section 2] ) a proof of the nonexistence of such a function field is given. This counterexample shows that the proof in [2] is wrong and so the list of algebraic function fields with class number one given in [2] should admit one more example.