2022/12/12 by Giuseppe Cotardo, Cotardo, Giuseppe · 1 citation
Computer Science · Engineering · #Advanced Wireless Communication Techniques #Coding theory and cryptography #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2212.06249
openalex publication_date 2022/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we introduce a new class of optimal tensor codes related to the Ravagnani-type anticodes, namely the j-tensor maximum rank distance codes. We show that it extends the family of j-maximum rank distance codes and contains the j-tensor binomial moment determined codes (with respect to the Ravagnani-type anticodes) as a proper subclass. We define and study the generalized zeta function for tensor codes. We establish connections between this object and the weight enumerator of a code with respect to the Ravagnani-type anticodes. We introduce a new refinement of the invariants of tensor codes exploiting the structure of product lattices of some classes of anticodes and we derive the corresponding MacWilliams identities. In this framework, we also define a multivariate version of the tensor weight enumerator and we establish relations with the corresponding zeta function. As an application we derive connections on the generalized tensor weights related to the Delsarte and Ravagnani-type anticodes.