On the minimum distance of negacyclic codes with two zeros

We investigate the minimum distance of q-ary negacyclic codes of length qm−12 generated by a product of two distinct minimal polynomials. A necessary and sufficient condition on the minimum distance of such negacyclic codes is given. Several classes of optimal quinary negacyclic codes with parameters [(5m−1)/2,(5m−1)/2−2m,4] are constructed. The dual codes of a subclass of the quinary negacyclic codes are studied. A comparison with cyclic codes is also presented.