Two classes of q-ary constacyclic BCH codes

Constacyclic BCH codes are an interesting subclass of constacyclic codes because of their important theoretical and practical value. The purpose of this paper is to study the parameters of cyclic BCH codes of length \(\varvec{n = q^{m} - 1}\) $\mathit{n}\mathbf{=}{\mathit{q}}^{\mathit{m}}\mathbf{-}\mathbf{1}$ and negacyclic BCH codes of length \(\varvec{n = \frac{q^{m} - 1}{2}}\) $\mathit{n}\mathbf{=}\frac{{\mathit{q}}^{\mathit{m}}\mathbf{-}\mathbf{1}}{\mathbf{2}}$ . We settle completely their dimensions. We also determine the minimum distances of a class of cyclic BCH codes of length \(\varvec{n = q^m - 1}\) $\mathit{n}\mathbf{=}{\mathit{q}}^{\mathit{m}}\mathbf{-}\mathbf{1}$ and give a lower bound on the minimum distances of other classes of constacyclic BCH codes. As seen by the code examples in this paper, the lower bound on the minimum distances of constacyclic BCH codes we gave is very close to the true minimum distances. These \(\varvec{q}\) $\mathit{q}$ -ary codes have good parameters in general.