On the classification of self-dual [20,10,9] codes over GF(7): In memory of Yutaka Hiramine

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2 Citations (Scopus)

Abstract

It is shown that the extended quadratic residue code of length 20 over GF(7) is a unique self-dual [20,10,9] code C such that the lattice obtained from C by Construction A is isomorphic to the 20-dimensional unimodular lattice D20+, up to equivalence. This is done by converting the classification of such self-dual codes to that of skew-Hadamard matrices of order 20.

Original languageEnglish
Pages (from-to)57-66
Number of pages10
JournalFinite Fields and their Applications
Volume42
DOIs
Publication statusPublished - 2016 Nov 1

Keywords

  • Self-dual code
  • Skew-Hadamard matrix
  • Unimodular lattice

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Engineering(all)
  • Applied Mathematics

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