Self-orthogonal codes from symmetric designs with fixed-point-free automorphisms

Masaaki Harada, Vladimir D. Tonchev

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)

Abstract

In this paper, we consider a method for constructing non-binary self-orthogonal codes from symmetric designs with fixed-point-free automorphisms. All codes over GF(3) and GF(7) derived from symmetric 2-(v,k,λ) designs with fixed-point-free automorphisms of order p for the parameters (v,k,λ,p)=(27,14,7,3),(40,27,18,5) and (45,12,3,5) are classified. A ternary [63,20,21] code with a record breaking minimum weight is constructed from the symmetric 2-(189,48,12) design found recently by Janko. Several codes over GF(5) and GF(7) that are either optimal or have the largest known minimum weight are constructed from designs obtained from known difference sets.

Original languageEnglish
Pages (from-to)81-90
Number of pages10
JournalDiscrete Mathematics
Volume264
Issue number1-3
DOIs
Publication statusPublished - 2003 Mar 6
Externally publishedYes

Keywords

  • Optimal codes
  • Self-orthogonal codes
  • Symmetric designs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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