2014/09/23 by Rolando Gómez Macedo, Macedo, Rolando Gómez, Felipe Zaldívar +1
Computer Science · Mathematics · #Advanced Data Storage Technologies #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1409.6382
arxiv created 2014/09/23 · openalex publication_date 2014/09/23 · arxiv updated 2014/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For the category of group codes, that generalizes the category of linear codes over a finite field, and with the generalized notions of direct sums and ndecomposable group codes, we prove that every MDS non trivial code, every perfect non trivial code, and every constant weight nondegenerate group code are indecomposable. We prove that every group code is a direct sum of indecomposable group codes, and using this result we obtain the automorphism groups of any group code in terms of its decomposition in indecomposable components. We conclude with the determination of the structure of decomposable cyclic group codes.