On LCD skew group codes

The article delves into the construction and properties of LCD skew group codes, a noncommutative generalization of cyclic codes introduced by Boucher et al. It begins by providing a historical context and definitions, emphasizing the larger number of skew cyclic codes compared to ordinary cyclic codes. The paper then introduces the notion of skew group rings and the Hamming weight of skew group codes, setting the stage for the construction of LCD and MDS codes. The authors present several propositions and theorems to establish properties of these codes, including their duality and self-adjoint nature. The article also provides concrete examples of LCD and MDS skew group codes, showcasing their potential applications in coding theory and cryptography. Additionally, the paper explores involutions in skew group rings and their role in constructing LCD codes. The authors conclude by discussing the dihedral case and providing examples of self-adjoint idempotents, further illustrating the richness and complexity of LCD skew group codes.