self-orthogonal code

Blackford (2008) [1] introduced the concept of negacyclic duadic codes over the field Fq, andclassified all self-dual negacyclic codes over Fq. In this paper, we define negacyclic duadic codes overring Fq +vFq and by using a Gray map on these codes, we get self-dual and self-orthogonal codes on thefield Fq. Also, we introduce some extensions of negacyclic duadic codes over ring Fq + vFq and presenttheir properties. Finally, we present some examples of negacyclic duadic codes over this ring and self-dualand self-orthogonal codes on the field Fq.