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

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Title: Rank-Metric Codes, Generalized Binomial Moments and their Zeta Functions
Authors: Byrne, EimearCotardo, GiuseppeRavagnani, Alberto
Permanent link: http://hdl.handle.net/10197/11529
Date: 1-Nov-2020
Online since: 2020-09-01T13:50:44Z
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.
Funding Details: Irish Research Council
metadata.dc.description.othersponsorship: Marie Curie Research Grants Scheme
Type of material: Journal Article
Journal: Linear Algebra and its Applications
Volume: 604
Start page: 92
End page: 128
Copyright (published version): 2020 Elsevier
Keywords: Rank-metric codeZeta functionBinomial momentsGeneralized rank weightsGeneralized rank weight distribution
DOI: 10.1016/j.laa.2020.06.002
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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