The lengths of Hermitian Self-Dual Extended Duadic Codes
  Duadic codes are a class of cyclic codes that generalizes quadratic residue codes from prime to composite lengths. For every prime power q, we characterize the integers n such that over the finite field with q^2 elements there is a duadic code of length n having an Hermitian self-dual parity-check extension.   We derive using analytic number theory asymptotic estimates for the number of such n as well as for the number of lengths for which duadic codes exist. 
Lilibeth Dicuangco, Pieter Moree, Patrick Sole