Some Local Cyclic codes based on compound decomposition of two polynomial rings

Local cyclic (LC) codes are block codes that are created on decompositions of polynomial rings. The biggest advantages of LC codes are: we can setup LC codes from all polynomial rings and there are numerous LC codes that can be found in a certain polynomial. All the researches of decompositions up to now have concentrated in only one polynomial ring. In order to increase the ability to setup new codes and find more optimal LC codes, this paper presents one type of compound decompositions that is performed on two polynomial rings. Two new LC codes constructed on this compound decomposition and some simulation results are also presented in this paper.