2020/02/15 by Elías Javier García Claro, Claro, Elias Javier Garcia, Horacio Tapia Recillas +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Information Theory (cs.IT) #Representation Theory (math.RT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2002.06407
openalex publication_date 2020/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Several relations and bounds for the dimension of principal ideals in group algebras are determined by analyzing minimal polynomials of regular representations. These results are used in the two last sections. First, in the context of semisimple group algebras, to compute, for any abelian code, an element with Hamming weight equal to its dimension. Finally, to get bounds on the minimum distance of certain MDS group codes. A relation between a class of group codes and MDS codes is presented. Examples illustrating the main results are provided.