On Linear Perfect b-Symbol Codes over Finite Fields

Kanat Abdukhalikov, Jiajie Chen, Rongquan Feng

Research output: Contribution to journalArticlepeer-review

Abstract

Motivated by the application of high-density data storage technologies, Cassuto and Blaum introduced codes for symbol-pair read channels in 2011, and Yaakobi et al. generalized the coding framework to that for b-symbol read channels where (Formula presented.) in 2016. In this paper, we establish a b-sphere-packing bound and present a recurrence relationship for the b-weight enumerator. We determine all parameters of linear perfect b-symbol e-error-correcting codes over (Formula presented.) for (Formula presented.) and show that for (Formula presented.), there exist at most finite such codes for a given (Formula presented.) and q. We construct a family of linear perfect b-symbol b-error-correcting codes over (Formula presented.) using constacyclic codes.

Original languageEnglish
Article number4128
JournalMathematics
Volume11
Issue number19
DOIs
Publication statusPublished - Oct 2023

Keywords

  • b-distance
  • b-sphere-packing bound
  • b-symbol code
  • b-weight
  • perfect b-symbol code

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • General Mathematics
  • Engineering (miscellaneous)

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