On bounds for codes over Frobenius rings under homogeneous weights

Marcus Greferath, Michael E. O'Sullivan

Research output: Contribution to journalArticleScientificpeer-review

17 Citations (Scopus)

Abstract

Homogeneous weight functions were introduced by Heise and Constantinescu (Lineare Codes über Restklassenringen ganzer Zahlen und ihre Automorphismen bezüglich einer verallgemeinerten Hamming-Metrik, Ph.D. Thesis, Technische Universität München, 1995; Problemy Peredachi Informatsii 33(3) (1997) 22–28). They appear as a natural generalization of the Hamming weight on finite fields and the Lee weight on Z4Z4 and have proven to be important in further papers (J. Combin. Theory 92 (2000) 17–28). This article develops a Plotkin and an Elias bound for (not necessarily linear) block codes on finite Frobenius rings that are equipped with this weight.
Original languageUndefined/Unknown
Pages (from-to)11-24
Number of pages14
JournalDiscrete Mathematics
Volume289
Issue number1-3
DOIs
Publication statusPublished - 2004
MoE publication typeA1 Journal article-refereed

Keywords

  • codes over rings
  • Frobenius rings
  • homogeneous weights
  • Plotkin bound
  • Elias boundSphere packing bound
  • Gilbert–Varshamov bound
  • ring codes

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