Determination for minimum symbol-pair and RT weights via torsional degrees of repeated-root cyclic codes

Research output: Contribution to journalArticlepeer-review

Abstract

There are various metrics for researching error-correcting codes. Especially, high-density data storage system gives the existence of inconsistency for the reading and writing process. The symbol-pair metric is motivated for outputs that have overlapping pairs of symbols in a certain channel. The Rosenbloom–Tsfasman (RT) metric is introduced since there exists a problem that is related to transmission over several parallel communication channels with some channels not available for the transmission. In this paper, we determine the minimum symbol-pair weight and RT weight of repeated-root cyclic codes over R=Fpm[u]/⟨u4⟩ of length n=pk. For the determination, we explicitly present third torsional degree for all different types of cyclic codes over R of length n.

Original languageEnglish
Pages (from-to)573-588
Number of pages16
JournalApplicable Algebra in Engineering, Communications and Computing
Volume35
Issue number4
DOIs
StatePublished - Jul 2024

Keywords

  • Cyclic code
  • Primary 94B15
  • RT weight
  • Secondary 94B05
  • Symbol-pair weight
  • Torsional degree

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