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

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

6 Citaten (Scopus)

Samenvatting

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.

Originele taal-2	Engels
Pagina's (van-tot)	92-128
Aantal pagina's	37
Tijdschrift	Linear Algebra and Its Applications
Volume	604
DOI's	https://doi.org/10.1016/j.laa.2020.06.002
Status	Gepubliceerd - 1 nov. 2020

Financiering

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.

Financiers	Financiernummer
European Union’s Horizon Europe research and innovation programme	740880
H2020 Marie Skłodowska-Curie Actions
Irish Research Council	GOIPG/2018/2534

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

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.",

keywords = "Binomial moments, Generalized rank weight distribution, Generalized rank weights, Rank-metric code, Zeta function",

author = "Eimear Byrne and Giuseppe Cotardo and Alberto Ravagnani",

year = "2020",

month = nov,

day = "1",

doi = "10.1016/j.laa.2020.06.002",

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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

UR - http://www.scopus.com/inward/record.url?scp=85086798873&partnerID=8YFLogxK

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DO - 10.1016/j.laa.2020.06.002

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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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