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

Eimear Byrne; Giuseppe Cotardo; Alberto Ravagnani

doi:10.1016/j.laa.2020.06.002

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

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

Mathematical Communication Theory

Research output: Contribution to journal › Article › Academic › peer-review

6 Citations (Scopus)

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 language	English
Pages (from-to)	92-128
Number of pages	37
Journal	Linear Algebra and Its Applications
Volume	604
DOIs	https://doi.org/10.1016/j.laa.2020.06.002
Publication status	Published - 1 Nov 2020

Funding

The author was supported by the Irish Research Council, grant n. GOIPG/2018/2534.The author was supported by the Marie Curie Research Grants Scheme, grant n. 740880.

Funders	Funder number
European Union's Horizon 2020 - Research and Innovation Framework Programme	740880
Marie Skłodowska‐Curie
Irish Research Council	GOIPG/2018/2534

Keywords

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

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10.1016/j.laa.2020.06.002

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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.",

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AU - Byrne, Eimear

AU - Cotardo, Giuseppe

AU - Ravagnani, Alberto

PY - 2020/11/1

Y1 - 2020/11/1

N2 - 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.

AB - 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.

KW - Binomial moments

KW - Generalized rank weight distribution

KW - Generalized rank weights

KW - Rank-metric code

KW - Zeta function

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DO - 10.1016/j.laa.2020.06.002

M3 - Article

AN - SCOPUS:85086798873

SN - 0024-3795

VL - 604

SP - 92

EP - 128

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

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

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Keywords

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