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. © 2013 Elsevier B.V.

New designs from circular nearrings

Benini, Anna;Frigeri, Achille
2013

Abstract

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. © 2013 Elsevier B.V.
Balanced incomplete block design; Binary codes; Circular nearring; Planar nearring; Discrete Mathematics and Combinatorics; Applied Mathematics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1063820
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