2025/10/31 by Steven T. Dougherty, Dougherty, S. T., Cristina Fernández-Córdoba +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Computer and information sciences #Finite Group Theory Research #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2510.27358
openalex publication_date 2025/10/31 · openalex created_date 2025/11/05 · openalex updated_date 2026/07/28
In this paper, we consider codes over finite fields, finite abelian groups, and finite Frobenius rings. For such codes, the complete weight enumerator and the Hamming weight enumerator serve as powerful tools. These two types of weight enumerators satisfy the MacWilliams relations. We define the weight enumerator of a code with respect to an equivalence relation and determine in which cases the MacWilliams relations hold for this weight enumerator. We also study some weight enumerators for specific equivalence relations.