New designs from circular nearrings

Nearrings are generalized rings in which addition is not in general abelian and only one distributive law holds. Some interesting combinatorial structures, as tactical configurations and balanced incomplete block designs (BIBDs) naturally arise when considering the class of planar and circular nearrings. We define the concept of disk and prove that in the case of field-generated planar circular nearrings it yields a BIBD. Such designs can be used in the construction of some classes of codes for which we are able to calculate the parameters.