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Designs, Codes and Cryptography

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25.10.2017

Rank metric codes and zeta functions

verfasst von: I. Blanco-Chacón, E. Byrne, I. Duursma, J. Sheekey

Erschienen in: Designs, Codes and Cryptography | Ausgabe 8/2018

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Abstract

We define the rank metric zeta function of a code as a generating function of its normalized q-binomial moments. We show that, as in the Hamming case, the zeta function gives a generating function for the weight enumerators of rank metric codes. We further prove a functional equation and derive an upper bound for the minimum distance in terms of the reciprocal roots of the zeta function. Finally, we show invariance under suitable puncturing and shortening operators and study the distribution of zeroes of the zeta function for a family of codes.

Vorheriger Artikel Flag-transitive point-primitive automorphism groups of non-symmetric 2-(v, k, 3) designs

Nächster Artikel On the (in)efficiency of non-interactive secure multiparty computation

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Titel: Rank metric codes and zeta functions
verfasst von: I. Blanco-Chacón
E. Byrne
I. Duursma
J. Sheekey
Publikationsdatum: 25.10.2017
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 8/2018
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-017-0423-8

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