BCH codes are a subclass of cyclic codes and widely employed in communication and storage systems. In this paper, we presented the first three largest q-cyclotomic coset leaders modulo \(\frac{q^{2m}-1}{q^{2}+1}\) , the second largest coset leader modulo \(\frac{q^{m}-1}{q+1}\) and obtained some almost optimal codes. A sufficient and necessary condition in terms of the designed distances \(\delta \) was presented to ensure that BCH codes are Hermitian dually-BCH codes with length \(\frac{q^{2m}-1}{q^{2}+1}\) . Furthermore, we presented the lower bounds on the minimum distances of their Hermitian dual codes and obtained some optimal codes.
