Composite matrices from group rings, composite G-codes and constructions of self-dual codes

Abstract In this work, we define composite matrices which are derived from group rings. We extend the idea of G -codes to -codes. show that these codes ideals in a ring, where ring is finite commutative Frobenius and an arbitrary group. prove dual -code also -code. quasi-composite Additionally, study generator matrices, consist identity matrices. Together with well known extension method, neighbour method its generalization, find extremal binary self-dual length 68 new weight enumerators for rare parameters $$\gamma =7,8$$ ? = 7 , 8 9. particular, 49 such codes. Moreover, inaccessible other construction