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, Eimear; Cotardo, Giuseppe; Ravagnani, 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 code; Zeta function; Binomial moments; Generalized rank weights; Generalized 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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