Some q-ary constacyclic BCH codes with length qm+12

Abstract

In this paper, we study some q-ary λ-constacyclic BCH codes of length $\frac{q^m+1}{2}$ with some large designed distances for $\mathrm{ord}\left(\lambda \right)=2$ and $2+\lceil \frac{4}{q-3}\rceil \le \mathrm{ord}\left(\lambda \right)\le q-1$ respectively, where q is an odd prime power and $\mathrm{ord}\left(\lambda \right)\left|\right(q-1)$. The dimensions and the lower bounds on the minimum distances of these codes are given by using recurrence relations and the introduced definitions of sequences. The code examples presented in this paper indicate that these codes have good parameters in general.