2022 Volume 76 Issue 2 Pages 441-450
A formal weight enumerator is a homogeneous polynomial in two variables which behaves like the Hamming weight enumerator of a self-dual linear code except that the coefficients are not necessarily non-negative integers. Chinen discovered several families of formal weight enumerators and investigated the validity of the Riemann hypothesis analogue for them. In this paper, the zeta polynomial is computed for Chinen's formal weight enumerators, and a simple criterion is given for the validity of the Riemann hypothesis analogue.
