On Plotkin-optimal codes over finite Frobenius rings

Marcus Greferath, Gary McGuire, Michael E. O'Sullivan

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We study the Plotkin bound for codes over a finite Frobenius ring R equipped with the homogeneous weight. We show that for codes meeting the Plotkin bound, the distribution on R induced by projection onto a coordinate has an interesting property. We present several constructions of codes meeting the Plotkin bound and of Plotkin-optimal codes. We also investigate the relationship between Butson–Hadamard matrices and codes over R meeting the Plotkin bound.
Original languageUndefined/Unknown
Pages (from-to)799-815
Number of pages17
JournalJOURNAL OF ALGEBRA AND ITS APPLICATIONS
Volume5
Issue number6
DOIs
Publication statusPublished - 2006
MoE publication typeA1 Journal article-refereed

Keywords

  • Frobenius ring
  • ring-linear codes
  • Plotkin bound
  • Butson–Hadamard matrix

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