English

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 ii-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 ii-MRD code and show that the ii-BMD codes form a proper subclass of the ii-MRD codes. Using the class of ii-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