Rank-Metric Codes, Generalized Binomial Moments and their Zeta Functions

Eimear Byrne, Giuseppe Cotardo (Corresponding author), Alberto Ravagnani

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

In this paper we introduce a new class of extremal codes, namely the i-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 i-MRD code and show that the i-BMD codes form a proper subclass of the i-MRD codes. Using the class of i-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.

Original languageEnglish
Pages (from-to)92-128
Number of pages37
JournalLinear Algebra and Its Applications
Volume604
DOIs
Publication statusPublished - 1 Nov 2020

Keywords

  • Binomial moments
  • Generalized rank weight distribution
  • Generalized rank weights
  • Rank-metric code
  • Zeta function

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