In this paper, by investigating the factor of the $x^n+1$, we deduce that the structure of the reversible negacyclic code over the finite field $\mathbb{ F}_{ q}$, where $q$ is an odd prime power. Though studying $q-$cyclotomic cosets modulo $2n$, we obtain the parameters of negacyclic BCH code of length $n=\frac{ q^\ell+1}{ 2}$ , $n=\frac{ q^m-1}{ 2(q-1)}$ and $n=\frac{ q^{ t\cdot2^\tau}-1}{ 2(q^t+1)}$. Some optimal linear codes from negacyclic codes are given. Finally, we discuss a class of MDS LCD negacyclic codes.
Categories: cs.IT math.IT