2024/04/08 by E. J. García-Claro, García-Claro, E. J.
Computer Science · Engineering · #11T71 #20C05 #94B60 #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Representation Theory (math.RT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2404.05775
openalex publication_date 2024/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An easily computable dimension (or ECD) group code in the group algebra \mathbbFqG is an ideal of dimension less than or equal to p=char(\mathbbFq) that is generated by an idempotent. This paper introduces an easily computable indecomposable dimension (or ECID) group algebra as a finite group algebra for which all group codes generated by primitive idempotents are ECD. Several characterizations are given for these algebras. In addition, some arithmetic conditions to determine whether a group algebra is ECID are presented, in the case it is semisimple. In the non-semisimple case, these algebras have finite representation type where the Sylow p-subgroups of the underlying group are simple. The dimension and some lower bounds for the minimum Hamming distance of group codes in these algebras are given together with some arithmetical tests of primitivity of idempotents. Examples illustrating the main results are presented.