Rank-Metric Codes, Generalized Binomial Moments and their Zeta Functions
Information Theory
2019-12-09 v2 math.IT
Abstract
In this paper we introduce a new class of extremal codes, namely the -BMD codes. We show that for this family several of the invariants are determined by the parameters of the underlying code. We refine and extend the notion of an -MRD code and show that the -BMD codes form a proper subclass of the -MRD codes. Using the class of -BMD codes we then obtain a relation between the generalized rank weight enumerator and its corresponding generalized zeta function. We also establish a MacWilliams identity for generalized rank weight distributions.
Keywords
Cite
@article{arxiv.1912.01928,
title = {Rank-Metric Codes, Generalized Binomial Moments and their Zeta Functions},
author = {Eimear Byrne and Giuseppe Cotardo and Alberto Ravagnani},
journal= {arXiv preprint arXiv:1912.01928},
year = {2019}
}
Comments
27 pages