Rank metric codes and zeta functions

I. Blanco-Chacón, E. Byrne, I. Duursma, J. Sheekey

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)1767-1792
Number of pages26
JournalDesigns, Codes, and Cryptography
Volume86
Issue number8
DOIs
StatePublished - Aug 1 2018

Keywords

  • Binomial moments
  • Gaussian binomial coefficient
  • Maximum-rank-distance
  • Rank metric code
  • Weight enumerator
  • Zeta function

ASJC Scopus subject areas

  • Computer Science Applications
  • Applied Mathematics

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